Daily Papers

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world da-tasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, po-tentially redefining the landscape of time series forecasting.

RNN-based methods have faced challenges in the Long-term Time Series Forecasting (LTSF) domain when dealing with excessively long look-back windows and forecast horizons. Consequently, the dominance in this domain has shifted towards Transformer, MLP, and CNN approaches. The substantial number of recurrent iterations are the fundamental reasons behind the limitations of RNNs in LTSF. To address these issues, we propose two novel strategies to reduce the number of iterations in RNNs for LTSF tasks: Segment-wise Iterations and Parallel Multi-step Forecasting (PMF). RNNs that combine these strategies, namely SegRNN, significantly reduce the required recurrent iterations for LTSF, resulting in notable improvements in forecast accuracy and inference speed. Extensive experiments demonstrate that SegRNN not only outperforms SOTA Transformer-based models but also reduces runtime and memory usage by more than 78%. These achievements provide strong evidence that RNNs continue to excel in LTSF tasks and encourage further exploration of this domain with more RNN-based approaches. The source code is coming soon.

Long-term Time Series Forecasting (LTSF) is critical for numerous real-world applications, such as electricity consumption planning, financial forecasting, and disease propagation analysis. LTSF requires capturing long-range dependencies between inputs and outputs, which poses significant challenges due to complex temporal dynamics and high computational demands. While linear models reduce model complexity by employing frequency domain decomposition, current approaches often assume stationarity and filter out high-frequency components that may contain crucial short-term fluctuations. In this paper, we introduce MMFNet, a novel model designed to enhance long-term multivariate forecasting by leveraging a multi-scale masked frequency decomposition approach. MMFNet captures fine, intermediate, and coarse-grained temporal patterns by converting time series into frequency segments at varying scales while employing a learnable mask to filter out irrelevant components adaptively. Extensive experimentation with benchmark datasets shows that MMFNet not only addresses the limitations of the existing methods but also consistently achieves good performance. Specifically, MMFNet achieves up to 6.0% reductions in the Mean Squared Error (MSE) compared to state-of-the-art models designed for multivariate forecasting tasks.

The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models in long-term time series forecasting (LTSF) tasks. Specifically, we introduce the Residual Cycle Forecasting (RCF) technique, which utilizes learnable recurrent cycles to model the inherent periodic patterns within sequences, and then performs predictions on the residual components of the modeled cycles. Combining RCF with a Linear layer or a shallow MLP forms the simple yet powerful method proposed in this paper, called CycleNet. CycleNet achieves state-of-the-art prediction accuracy in multiple domains including electricity, weather, and energy, while offering significant efficiency advantages by reducing over 90% of the required parameter quantity. Furthermore, as a novel plug-and-play technique, the RCF can also significantly improve the prediction accuracy of existing models, including PatchTST and iTransformer. The source code is available at: https://github.com/ACAT-SCUT/CycleNet.

Recently, there has been a growing interest in Long-term Time Series Forecasting (LTSF), which involves predicting long-term future values by analyzing a large amount of historical time-series data to identify patterns and trends. There exist significant challenges in LTSF due to its complex temporal dependencies and high computational demands. Although Transformer-based models offer high forecasting accuracy, they are often too compute-intensive to be deployed on devices with hardware constraints. On the other hand, the linear models aim to reduce the computational overhead by employing either decomposition methods in the time domain or compact representations in the frequency domain. In this paper, we propose MixLinear, an ultra-lightweight multivariate time series forecasting model specifically designed for resource-constrained devices. MixLinear effectively captures both temporal and frequency domain features by modeling intra-segment and inter-segment variations in the time domain and extracting frequency variations from a low-dimensional latent space in the frequency domain. By reducing the parameter scale of a downsampled n-length input/output one-layer linear model from O(n^2) to O(n), MixLinear achieves efficient computation without sacrificing accuracy. Extensive evaluations with four benchmark datasets show that MixLinear attains forecasting performance comparable to, or surpassing, state-of-the-art models with significantly fewer parameters (0.1K), which makes it well-suited for deployment on devices with limited computational capacity.

Recently, there has been a surge of Transformer-based solutions for the long-term time series forecasting (LTSF) task. Despite the growing performance over the past few years, we question the validity of this line of research in this work. Specifically, Transformers is arguably the most successful solution to extract the semantic correlations among the elements in a long sequence. However, in time series modeling, we are to extract the temporal relations in an ordered set of continuous points. While employing positional encoding and using tokens to embed sub-series in Transformers facilitate preserving some ordering information, the nature of the permutation-invariant self-attention mechanism inevitably results in temporal information loss. To validate our claim, we introduce a set of embarrassingly simple one-layer linear models named LTSF-Linear for comparison. Experimental results on nine real-life datasets show that LTSF-Linear surprisingly outperforms existing sophisticated Transformer-based LTSF models in all cases, and often by a large margin. Moreover, we conduct comprehensive empirical studies to explore the impacts of various design elements of LTSF models on their temporal relation extraction capability. We hope this surprising finding opens up new research directions for the LTSF task. We also advocate revisiting the validity of Transformer-based solutions for other time series analysis tasks (e.g., anomaly detection) in the future. Code is available at: https://github.com/cure-lab/LTSF-Linear.

In recent work on time-series prediction, Transformers and even large language models have garnered significant attention due to their strong capabilities in sequence modeling. However, in practical deployments, time-series prediction often requires operation in resource-constrained environments, such as edge devices, which are unable to handle the computational overhead of large models. To address such scenarios, some lightweight models have been proposed, but they exhibit poor performance on non-stationary sequences. In this paper, we propose SWIFT, a lightweight model that is not only powerful, but also efficient in deployment and inference for Long-term Time Series Forecasting (LTSF). Our model is based on three key points: (i) Utilizing wavelet transform to perform lossless downsampling of time series. (ii) Achieving cross-band information fusion with a learnable filter. (iii) Using only one shared linear layer or one shallow MLP for sub-series' mapping. We conduct comprehensive experiments, and the results show that SWIFT achieves state-of-the-art (SOTA) performance on multiple datasets, offering a promising method for edge computing and deployment in this task. Moreover, it is noteworthy that the number of parameters in SWIFT-Linear is only 25\% of what it would be with a single-layer linear model for time-domain prediction. Our code is available at https://github.com/LancelotXWX/SWIFT.

Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced architecture specifically designed for multivariate LTSF modelling. ARM employs Adaptive Univariate Effect Learning (AUEL), Random Dropping (RD) training strategy, and Multi-kernel Local Smoothing (MKLS), to better handle individual series temporal patterns and correctly learn inter-series dependencies. ARM demonstrates superior performance on multiple benchmarks without significantly increasing computational costs compared to vanilla Transformer, thereby advancing the state-of-the-art in LTSF. ARM is also generally applicable to other LTSF architecture beyond vanilla Transformer.

Time series forecasting plays a crucial role in data mining, driving rapid advancements across numerous industries. With the emergence of large models, time series foundation models (TSFMs) have exhibited remarkable generalization capabilities, such as zero-shot learning, through large-scale pre-training. Meanwhile, Retrieval-Augmented Generation (RAG) methods have been widely employed to enhance the performance of foundation models on unseen data, allowing models to access to external knowledge. In this paper, we introduce TimeRAF, a Retrieval-Augmented Forecasting model that enhance zero-shot time series forecasting through retrieval-augmented techniques. We develop customized time series knowledge bases that are tailored to the specific forecasting tasks. TimeRAF employs an end-to-end learnable retriever to extract valuable information from the knowledge base. Additionally, we propose Channel Prompting for knowledge integration, which effectively extracts relevant information from the retrieved knowledge along the channel dimension. Extensive experiments demonstrate the effectiveness of our model, showing significant improvement across various domains and datasets.

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, including quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a ProbSparse self-attention mechanism, which achieves O(L log L) in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.

In this work, we leverage pre-trained Large Language Models (LLMs) to enhance time-series forecasting. Mirroring the growing interest in unifying models for Natural Language Processing and Computer Vision, we envision creating an analogous model for long-term time-series forecasting. Due to limited large-scale time-series data for building robust foundation models, our approach LLM4TS focuses on leveraging the strengths of pre-trained LLMs. By combining time-series patching with temporal encoding, we have enhanced the capability of LLMs to handle time-series data effectively. Inspired by the supervised fine-tuning in chatbot domains, we prioritize a two-stage fine-tuning process: first conducting supervised fine-tuning to orient the LLM towards time-series data, followed by task-specific downstream fine-tuning. Furthermore, to unlock the flexibility of pre-trained LLMs without extensive parameter adjustments, we adopt several Parameter-Efficient Fine-Tuning (PEFT) techniques. Drawing on these innovations, LLM4TS has yielded state-of-the-art results in long-term forecasting. Our model has also shown exceptional capabilities as both a robust representation learner and an effective few-shot learner, thanks to the knowledge transferred from the pre-trained LLM.

Foundation models have emerged as a promising approach in time series forecasting (TSF). Existing approaches either fine-tune large language models (LLMs) or build large-scale time-series datasets to develop TSF foundation models. However, these methods face challenges due to the severe cross-domain gap or in-domain heterogeneity. In this paper, we explore a new road to building a TSF foundation model from rich and high-quality natural images, based on the intrinsic similarities between images and time series. To bridge the gap between the two domains, we reformulate the TSF task as an image reconstruction task, which is further processed by a visual masked autoencoder (MAE) self-supervised pre-trained on the ImageNet dataset. Surprisingly, without further adaptation in the time-series domain, the proposed VisionTS could achieve superior zero-shot forecasting performance compared to existing TSF foundation models. With minimal fine-tuning, VisionTS could further improve the forecasting and achieve state-of-the-art performance in most cases. These findings suggest that visual models could be a free lunch for TSF and highlight the potential for future cross-domain research between computer vision and TSF. Our code is publicly available at https://github.com/Keytoyze/VisionTS.

Large Language Models (LLMs) and Foundation Models (FMs) have recently become prevalent for time series forecasting tasks. While fine-tuning LLMs enables domain adaptation, they often struggle to generalize across diverse and unseen datasets. Moreover, existing Time Series Foundation Models (TSFMs) still face challenges in handling non-stationary dynamics and distribution shifts, largely due to the lack of effective mechanisms for adaptation. To this end, we present TS-RAG, a retrieval-augmented generation framework for time series forecasting that enhances the generalization and interpretability of TSFMs. Specifically, TS-RAG leverages pre-trained time series encoders to retrieve semantically relevant segments from a dedicated knowledge base, enriching the contextual representation of the input query. Furthermore, we propose an Adaptive Retrieval Mixer (ARM) module that dynamically fuses the retrieved patterns with the TSFM's internal representation, improving forecasting accuracy without requiring task-specific fine-tuning. Thorough empirical studies on seven public benchmark datasets demonstrate that TS-RAG achieves state-of-the-art zero-shot forecasting performance, outperforming the existing TSFMs by up to 6.84% across diverse domains while also providing desirable interpretability. Our code and data are available at: https://github.com/UConn-DSIS/TS-RAG

Time Series Foundation Models (TSFMs) represent a new paradigm for time-series forecasting, promising zero-shot predictions without the need for task-specific training or fine-tuning. However, similar to Large Language Models (LLMs), the evaluation of TSFMs is challenging: as training corpora grow increasingly large, it becomes difficult to ensure the integrity of the test sets used for benchmarking. An investigation of existing TSFM evaluation studies identifies two kinds of information leakage: (1) train-test sample overlaps arising from the multi-purpose reuse of datasets and (2) temporal overlap of correlated train and test series. Ignoring these forms of information leakage when benchmarking TSFMs risks producing overly optimistic performance estimates that fail to generalize to real-world settings. We therefore argue for the development of novel evaluation methodologies that avoid pitfalls already observed in both LLM and classical time-series benchmarking, and we call on the research community to adopt principled approaches to safeguard the integrity of TSFM evaluation.

Time Series Foundation Models (TSFMs) have recently achieved state-of-the-art performance in univariate forecasting on new time series simply by conditioned on a brief history of past values. Their success demonstrates that large-scale pretraining across diverse domains can acquire the inductive bias to generalize from temporal patterns in a brief history. However, most TSFMs are unable to leverage covariates -- future-available exogenous variables critical for accurate forecasting in many applications -- due to their domain-specific nature and the lack of associated inductive bias. We propose TFMAdapter, a lightweight, instance-level adapter that augments TSFMs with covariate information without fine-tuning. Instead of retraining, TFMAdapter operates on the limited history provided during a single model call, learning a non-parametric cascade that combines covariates with univariate TSFM forecasts. However, such learning would require univariate forecasts at all steps in the history, requiring too many calls to the TSFM. To enable training on the full historical context while limiting TSFM invocations, TFMAdapter uses a two-stage method: (1) generating pseudo-forecasts with a simple regression model, and (2) training a Gaussian Process regressor to refine predictions using both pseudo- and TSFM forecasts alongside covariates. Extensive experiments on real-world datasets demonstrate that TFMAdapter consistently outperforms both foundation models and supervised baselines, achieving a 24-27\% improvement over base foundation models with minimal data and computational overhead. Our results highlight the potential of lightweight adapters to bridge the gap between generic foundation models and domain-specific forecasting needs.

Time series forecasting (TSF) is critical in domains like energy, finance, healthcare, and logistics, requiring models that generalize across diverse datasets. Large pre-trained models such as Chronos and Time-MoE show strong zero-shot (ZS) performance but suffer from high computational costs. In this work, We introduce Super-Linear, a lightweight and scalable mixture-of-experts (MoE) model for general forecasting. It replaces deep architectures with simple frequency-specialized linear experts, trained on resampled data across multiple frequency regimes. A lightweight spectral gating mechanism dynamically selects relevant experts, enabling efficient, accurate forecasting. Despite its simplicity, Super-Linear matches state-of-the-art performance while offering superior efficiency, robustness to various sampling rates, and enhanced interpretability. The implementation of Super-Linear is available at https://github.com/azencot-group/SuperLinear{https://github.com/azencot-group/SuperLinear}

We present a joint forecasting framework for time series prediction that contrasts with traditional direct or recursive methods. This framework achieves state-of-the-art performance for our designed foundation model, YingLong, and reveals a novel scaling effect: longer outputs significantly enhance model accuracy due to delayed chain-of-thought reasoning in our non-causal approach. YingLong is a non-causal, bidirectional attention encoder-only transformer trained through masked token recovery, aligning more effectively with language understanding tasks than with generation tasks. Additionally, we boost performance by tackling output variance with a multi-input ensemble. We release four foundation models ranging from 6M to 300M parameters, demonstrating superior results in zero-shot tasks on the ETT and Weather datasets. YingLong achieves more than 60% best performance. To ensure generalizability, we assessed the models using the GIFT-Eval benchmark, which comprises 23 time series datasets across 7 domains. Yinglong significantly outperformed the best time-series foundation models, end-to-end trained models by 14% and 44% in rank respectively.The pretrained 300M model is available at https://huggingface.co/qcw1314/YingLong_300m

Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformer-based models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields state-of-the-art accuracy, with a 38% relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. Code is available at this repository: https://github.com/thuml/Autoformer.

Existing works on general time series forecasting build foundation models with heavy model parameters through large-scale multi-source pre-training. These models achieve superior generalization ability across various datasets at the cost of significant computational burdens and limitations in resource-constrained scenarios. This paper introduces LightGTS, a lightweight general time series forecasting model designed from the perspective of consistent periodical modeling. To handle diverse scales and intrinsic periods in multi-source pre-training, we introduce Periodical Tokenization, which extracts consistent periodic patterns across different datasets with varying scales. To better utilize the periodicity in the decoding process, we further introduce Periodical Parallel Decoding, which leverages historical tokens to improve forecasting. Based on the two techniques above which fully leverage the inductive bias of periods inherent in time series, LightGTS uses a lightweight model to achieve outstanding performance on general time series forecasting. It achieves state-of-the-art forecasting performance on 9 real-world benchmarks in both zero-shot and full-shot settings with much better efficiency compared with existing time series foundation models.

Recently, deep learning has driven significant advancements in multivariate time series forecasting (MTSF) tasks. However, much of the current research in MTSF tends to evaluate models from a holistic perspective, which obscures the individual contributions and leaves critical issues unaddressed. Adhering to the current modeling paradigms, this work bridges these gaps by systematically decomposing deep MTSF methods into their core, fine-grained components like series-patching tokenization, channel-independent strategy, attention modules, or even Large Language Models and Time-series Foundation Models. Through extensive experiments and component-level analysis, our work offers more profound insights than previous benchmarks that typically discuss models as a whole. Furthermore, we propose a novel automated solution called TSGym for MTSF tasks. Unlike traditional hyperparameter tuning, neural architecture searching or fixed model selection, TSGym performs fine-grained component selection and automated model construction, which enables the creation of more effective solutions tailored to diverse time series data, therefore enhancing model transferability across different data sources and robustness against distribution shifts. Extensive experiments indicate that TSGym significantly outperforms existing state-of-the-art MTSF and AutoML methods. All code is publicly available on https://github.com/SUFE-AILAB/TSGym.

Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To fully revitalize the general-purpose token transition and multi-step generation capability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which projects time series into the embedding space of language tokens and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability with larger LLMs. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By introducing LLM-embedded textual timestamps, AutoTimes can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over 5times training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

Deep learning (e.g., Transformer) has been widely and successfully used in multivariate time series forecasting (MTSF). Unlike existing methods that focus on training models from a single modal of time series input, large language models (LLMs) based MTSF methods with cross-modal text and time series input have recently shown great superiority, especially with limited temporal data. However, current LLM-based MTSF methods usually focus on adapting and fine-tuning LLMs, while neglecting the distribution discrepancy between textual and temporal input tokens, thus leading to sub-optimal performance. To address this issue, we propose a novel Cross-Modal LLM Fine-Tuning (CALF) framework for MTSF by reducing the distribution discrepancy between textual and temporal data, which mainly consists of the temporal target branch with temporal input and the textual source branch with aligned textual input. To reduce the distribution discrepancy, we develop the cross-modal match module to first align cross-modal input distributions. Additionally, to minimize the modality distribution gap in both feature and output spaces, feature regularization loss is developed to align the intermediate features between the two branches for better weight updates, while output consistency loss is introduced to allow the output representations of both branches to correspond effectively. Thanks to the modality alignment, CALF establishes state-of-the-art performance for both long-term and short-term forecasting tasks with low computational complexity, and exhibiting favorable few-shot and zero-shot abilities similar to that in LLMs. Code is available at https://github.com/Hank0626/LLaTA.

Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historical-value models. Yet, despite the attractive properties of time-index models, such as being able to model the continuous nature of underlying time series dynamics, little attention has been given to them. Indeed, while naive deep time-index models are far more expressive than the manually predefined function representations of classical time-index models, they are inadequate for forecasting, being unable to generalize to unseen time steps due to the lack of inductive bias. In this paper, we propose DeepTime, a meta-optimization framework to learn deep time-index models which overcome these limitations, yielding an efficient and accurate forecasting model. Extensive experiments on real world datasets in the long sequence time-series forecasting setting demonstrate that our approach achieves competitive results with state-of-the-art methods, and is highly efficient. Code is available at https://github.com/salesforce/DeepTime.

Time series forecasting (TSF) remains a challenging and largely unsolved problem in machine learning, despite significant recent efforts leveraging Large Language Models (LLMs), which predominantly rely on Transformer architectures. Empirical evidence consistently shows that even powerful Transformers often fail to outperform much simpler models, e.g., linear models, on TSF tasks; however, a rigorous theoretical understanding of this phenomenon remains limited. In this paper, we provide a theoretical analysis of Transformers' limitations for TSF through the lens of In-Context Learning (ICL) theory. Specifically, under AR(p) data, we establish that: (1) Linear Self-Attention (LSA) models cannot achieve lower expected MSE than classical linear models for in-context forecasting; (2) as the context length approaches to infinity, LSA asymptotically recovers the optimal linear predictor; and (3) under Chain-of-Thought (CoT) style inference, predictions collapse to the mean exponentially. We empirically validate these findings through carefully designed experiments. Our theory not only sheds light on several previously underexplored phenomena but also offers practical insights for designing more effective forecasting architectures. We hope our work encourages the broader research community to revisit the fundamental theoretical limitations of TSF and to critically evaluate the direct application of increasingly sophisticated architectures without deeper scrutiny.

Time series forecasting is central to decision-making in domains as diverse as energy, finance, climate, and public health. In practice, forecasters face thousands of short, noisy series that vary in frequency, quality, and horizon, where the dominant cost lies not in model fitting, but in the labor-intensive preprocessing, validation, and ensembling required to obtain reliable predictions. Prevailing statistical and deep learning models are tailored to specific datasets or domains and generalize poorly. A general, domain-agnostic framework that minimizes human intervention is urgently in demand. In this paper, we introduce TimeSeriesScientist (TSci), the first LLM-driven agentic framework for general time series forecasting. The framework comprises four specialized agents: Curator performs LLM-guided diagnostics augmented by external tools that reason over data statistics to choose targeted preprocessing; Planner narrows the hypothesis space of model choice by leveraging multi-modal diagnostics and self-planning over the input; Forecaster performs model fitting and validation and, based on the results, adaptively selects the best model configuration as well as ensemble strategy to make final predictions; and Reporter synthesizes the whole process into a comprehensive, transparent report. With transparent natural-language rationales and comprehensive reports, TSci transforms the forecasting workflow into a white-box system that is both interpretable and extensible across tasks. Empirical results on eight established benchmarks demonstrate that TSci consistently outperforms both statistical and LLM-based baselines, reducing forecast error by an average of 10.4% and 38.2%, respectively. Moreover, TSci produces a clear and rigorous report that makes the forecasting workflow more transparent and interpretable.

The success of large pretrained models in natural language processing (NLP) and computer vision (CV) has opened new avenues for constructing foundation models for time series forecasting (TSF). Traditional TSF foundation models rely heavily on numerical data fitting. In contrast, the human brain is inherently skilled at processing visual information, prefer predicting future trends by observing visualized sequences. From a biomimetic perspective, utilizing models to directly process numerical sequences might not be the most effective route to achieving Artificial General Intelligence (AGI). This paper proposes ViTime, a novel Visual Intelligence-based foundation model for TSF. ViTime overcomes the limitations of numerical time series data fitting by utilizing visual data processing paradigms and employs a innovative data synthesis method during training, called Real Time Series (RealTS). Experiments on a diverse set of previously unseen forecasting datasets demonstrate that ViTime achieves state-of-the-art zero-shot performance, even surpassing the best individually trained supervised models in some situations. These findings suggest that visual intelligence can significantly enhance time series analysis and forecasting, paving the way for more advanced and versatile models in the field. The code for our framework is accessible at https://github.com/IkeYang/ViTime.

Financial time series forecasting is central to trading, portfolio optimization, and risk management, yet it remains challenging due to noisy, non-stationary, and heterogeneous data. Recent advances in time series foundation models (TSFMs), inspired by large language models, offer a new paradigm for learning generalizable temporal representations from large and diverse datasets. This paper presents the first comprehensive empirical study of TSFMs in global financial markets. Using a large-scale dataset of daily excess returns across diverse markets, we evaluate zero-shot inference, fine-tuning, and pre-training from scratch against strong benchmark models. We find that off-the-shelf pre-trained TSFMs perform poorly in zero-shot and fine-tuning settings, whereas models pre-trained from scratch on financial data achieve substantial forecasting and economic improvements, underscoring the value of domain-specific adaptation. Increasing the dataset size, incorporating synthetic data augmentation, and applying hyperparameter tuning further enhance performance.

Time series are generated in diverse domains such as economic, traffic, health, and energy, where forecasting of future values has numerous important applications. Not surprisingly, many forecasting methods are being proposed. To ensure progress, it is essential to be able to study and compare such methods empirically in a comprehensive and reliable manner. To achieve this, we propose TFB, an automated benchmark for Time Series Forecasting (TSF) methods. TFB advances the state-of-the-art by addressing shortcomings related to datasets, comparison methods, and evaluation pipelines: 1) insufficient coverage of data domains, 2) stereotype bias against traditional methods, and 3) inconsistent and inflexible pipelines. To achieve better domain coverage, we include datasets from 10 different domains: traffic, electricity, energy, the environment, nature, economic, stock markets, banking, health, and the web. We also provide a time series characterization to ensure that the selected datasets are comprehensive. To remove biases against some methods, we include a diverse range of methods, including statistical learning, machine learning, and deep learning methods, and we also support a variety of evaluation strategies and metrics to ensure a more comprehensive evaluations of different methods. To support the integration of different methods into the benchmark and enable fair comparisons, TFB features a flexible and scalable pipeline that eliminates biases. Next, we employ TFB to perform a thorough evaluation of 21 Univariate Time Series Forecasting (UTSF) methods on 8,068 univariate time series and 14 Multivariate Time Series Forecasting (MTSF) methods on 25 datasets. The benchmark code and data are available at https://github.com/decisionintelligence/TFB. We have also launched an online time series leaderboard: https://decisionintelligence.github.io/OpenTS/OpenTS-Bench/.

Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that Time-LLM is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios.

Time series forecasting is a foundational task across domains, such as finance, healthcare, and environmental monitoring. While recent advances in Time Series Foundation Models (TSFMs) have demonstrated strong generalisation through large-scale pretraining, existing models operate predominantly in a unimodal setting, ignoring the rich multimodal context, such as visual and textual signals, that often accompanies time series data in real-world scenarios. This paper introduces a novel parameter-efficient multimodal framework, UniCast, that extends TSFMs to jointly leverage time series, vision, and text modalities for enhanced forecasting performance. Our method integrates modality-specific embeddings from pretrained Vision and Text Encoders with a frozen TSFM via soft prompt tuning, enabling efficient adaptation with minimal parameter updates. This design not only preserves the generalisation strength of the foundation model but also enables effective cross-modal interaction. Extensive experiments across diverse time-series forecasting benchmarks demonstrate that UniCast consistently and significantly outperforms all existing TSFM baselines. The findings highlight the critical role of multimodal context in advancing the next generation of general-purpose time series forecasters.

Over the past years, foundation models have caused a paradigm shift in machine learning due to their unprecedented capabilities for zero-shot and few-shot generalization. However, despite the success of foundation models in modalities such as natural language processing and computer vision, the development of foundation models for time series forecasting has lagged behind. We present Lag-Llama, a general-purpose foundation model for univariate probabilistic time series forecasting based on a decoder-only transformer architecture that uses lags as covariates. Lag-Llama is pretrained on a large corpus of diverse time series data from several domains, and demonstrates strong zero-shot generalization capabilities compared to a wide range of forecasting models on downstream datasets across domains. Moreover, when fine-tuned on relatively small fractions of such previously unseen datasets, Lag-Llama achieves state-of-the-art performance, outperforming prior deep learning approaches, emerging as the best general-purpose model on average. Lag-Llama serves as a strong contender to the current state-of-art in time series forecasting and paves the way for future advancements in foundation models tailored to time series data.

Time series forecasting is a long-standing and highly challenging research topic. Recently, driven by the rise of large language models (LLMs), research has increasingly shifted from purely time series methods toward harnessing textual modalities to enhance forecasting performance. However, the vast discrepancy between text and temporal data often leads current multimodal architectures to over-emphasise one modality while neglecting the other, resulting in information loss that harms forecasting performance. To address this modality imbalance, we introduce BALM-TSF (Balanced Multimodal Alignment for LLM-Based Time Series Forecasting), a lightweight time series forecasting framework that maintains balance between the two modalities. Specifically, raw time series are processed by the time series encoder, while descriptive statistics of raw time series are fed to an LLM with learnable prompt, producing compact textual embeddings. To ensure balanced cross-modal context alignment of time series and textual embeddings, a simple yet effective scaling strategy combined with a contrastive objective then maps these textual embeddings into the latent space of the time series embeddings. Finally, the aligned textual semantic embeddings and time series embeddings are together integrated for forecasting. Extensive experiments on standard benchmarks show that, with minimal trainable parameters, BALM-TSF achieves state-of-the-art performance in both long-term and few-shot forecasting, confirming its ability to harness complementary information from text and time series. Code is available at https://github.com/ShiqiaoZhou/BALM-TSF.

Motivated by recent advances in large language models for Natural Language Processing (NLP), we design a time-series foundation model for forecasting whose out-of-the-box zero-shot performance on a variety of public datasets comes close to the accuracy of state-of-the-art supervised forecasting models for each individual dataset. Our model is based on pretraining a patched-decoder style attention model on a large time-series corpus, and can work well across different forecasting history lengths, prediction lengths and temporal granularities.

Accurate household electricity short-term load forecasting (STLF) is key to future and sustainable energy systems. While various studies have analyzed statistical, machine learning, or deep learning approaches for household electricity STLF, recently proposed time series foundation models such as Chronos, TimesFM or Time-MoE promise a new approach for household electricity STLF. These models are trained on a vast amount of time series data and are able to forecast time series without explicit task-specific training (zero-shot learning). In this study, we benchmark the forecasting capabilities of time series foundation models compared to Trained-from-Scratch (TFS) Transformer-based approaches. Our results suggest that foundation models perform comparably to TFS Transformer models, while certain time series foundation models outperform all TFS models when the input size increases. At the same time, they require less effort, as they need no domain-specific training and only limited contextual data for inference.

Time series foundation models (TSFMs) have emerged as a powerful paradigm for time series analysis, driven by large-scale pretraining on diverse data corpora. However, time series inherently exhibit heterogeneous information density over time, influenced by system states and signal complexity, presenting significant modeling challenges especially in a zero-shot scenario. Current TSFMs rely on non-adaptive processing pipelines that fail to capture this dynamic nature. For example, common tokenization strategies such as fixed-size patching enforce rigid observational granularity, limiting their ability to adapt to varying information densities. Similarly, conventional positional encodings impose a uniform temporal scale, making it difficult to model diverse periodicities and trends across series. To overcome these limitations, we propose Kairos, a flexible TSFM framework that integrates a dynamic patching tokenizer and an instance-adaptive positional embedding. Kairos adaptively selects tokenization granularity and tailors positional encodings to the unique characteristics of each time series instance. Trained on a large-scale Predictability-Stratified Time Series (PreSTS) corpus comprising over 300 billion time points and adopting a multi-patch prediction strategy in the inference stage, Kairos achieves superior performance with much fewer parameters on two common zero-shot benchmarks, GIFT-Eval and the Time-Series-Library benchmark, consistently outperforming established methods across diverse tasks. The project page is at https://foundation-model-research.github.io/Kairos .

Financial time series forecasting is particularly challenging for transformer-based time series foundation models (TSFMs) due to non-stationarity, heavy-tailed distributions, and high-frequency noise present in data. Low-rank adaptation (LoRA) has become a popular parameter-efficient method for adapting pre-trained TSFMs to downstream data domains. However, it still underperforms in financial data, as it preserves the network architecture and training objective of TSFMs rather than complementing the foundation model. To further enhance TSFMs, we propose a novel refinement module, RefineBridge, built upon a tractable Schrödinger Bridge (SB) generative framework. Given the forecasts of TSFM as generative prior and the observed ground truths as targets, RefineBridge learns context-conditioned stochastic transport maps to improve TSFM predictions, iteratively approaching the ground-truth target from even a low-quality prior. Simulations on multiple financial benchmarks demonstrate that RefineBridge consistently improves the performance of state-of-the-art TSFMs across different prediction horizons.

While LLMs have demonstrated remarkable potential in time series forecasting, their practical deployment remains constrained by excessive computational demands and memory footprints. Existing LLM-based approaches typically suffer from three critical limitations: Inefficient parameter utilization in handling numerical time series patterns; Modality misalignment between continuous temporal signals and discrete text embeddings; and Inflexibility for real-time expert knowledge integration. We present SMETimes, the first systematic investigation of sub-3B parameter SLMs for efficient and accurate time series forecasting. Our approach centers on three key innovations: A statistically-enhanced prompting mechanism that bridges numerical time series with textual semantics through descriptive statistical features; A adaptive fusion embedding architecture that aligns temporal patterns with language model token spaces through learnable parameters; And a dynamic mixture-of-experts framework enabled by SLMs' computational efficiency, adaptively combining base predictions with domain-specific models. Extensive evaluations across seven benchmark datasets demonstrate that our 3B-parameter SLM achieves state-of-the-art performance on five primary datasets while maintaining 3.8x faster training and 5.2x lower memory consumption compared to 7B-parameter LLM baselines. Notably, the proposed model exhibits better learning capabilities, achieving 12.3% lower MSE than conventional LLM. Ablation studies validate that our statistical prompting and cross-modal fusion modules respectively contribute 15.7% and 18.2% error reduction in long-horizon forecasting tasks. By redefining the efficiency-accuracy trade-off landscape, this work establishes SLMs as viable alternatives to resource-intensive LLMs for practical time series forecasting. Code and models are available at https://github.com/xiyan1234567/SMETimes.

Recent research has shown that large language models (LLMs) can be effectively used for real-world time series forecasting due to their strong natural language understanding capabilities. However, aligning time series into semantic spaces of LLMs comes with high computational costs and inference complexity, particularly for long-range time series generation. Building on recent advancements in using linear models for time series, this paper introduces an LLM-enhanced mixture of linear experts for precise and efficient time series forecasting. This approach involves developing a mixture of linear experts with multiple lookback lengths and a new multimodal fusion mechanism. The use of a mixture of linear experts is efficient due to its simplicity, while the multimodal fusion mechanism adaptively combines multiple linear experts based on the learned features of the text modality from pre-trained large language models. In experiments, we rethink the need to align time series to LLMs by existing time-series large language models and further discuss their efficiency and effectiveness in time series forecasting. Our experimental results show that the proposed LeMoLE model presents lower prediction errors and higher computational efficiency than existing LLM models.

Foundation models have become increasingly popular for forecasting due to their ability to provide predictions without requiring a lot of training data. In this work, we demonstrate how TabPFN-v2, a general tabular foundation model, can be effectively applied to time series forecasting. We introduce TabPFN-TS, a simple method that combines TabPFN-v2 with lightweight feature engineering to enable both point and probabilistic forecasting. Despite its simplicity and compact size (11M parameters), TabPFN-TS achieves top rank on the public GIFT-Eval leaderboard in both forecasting tasks. Through ablation studies, we investigate factors contributing to this surprising effectiveness, especially considering TabPFN-v2 was pretrained solely on synthetic tabular data with no exposure to time series. Our results highlights the potential of tabular foundation models like TabPFN-v2 as a valuable new approach for time series forecasting. Our implementation is available at https://github.com/PriorLabs/tabpfn-time-series.

Time series forecasting has played the key role in different industrial, including finance, traffic, energy, and healthcare domains. While existing literatures have designed many sophisticated architectures based on RNNs, GNNs, or Transformers, another kind of approaches based on multi-layer perceptrons (MLPs) are proposed with simple structure, low complexity, and {superior performance}. However, most MLP-based forecasting methods suffer from the point-wise mappings and information bottleneck, which largely hinders the forecasting performance. To overcome this problem, we explore a novel direction of applying MLPs in the frequency domain for time series forecasting. We investigate the learned patterns of frequency-domain MLPs and discover their two inherent characteristic benefiting forecasting, (i) global view: frequency spectrum makes MLPs own a complete view for signals and learn global dependencies more easily, and (ii) energy compaction: frequency-domain MLPs concentrate on smaller key part of frequency components with compact signal energy. Then, we propose FreTS, a simple yet effective architecture built upon Frequency-domain MLPs for Time Series forecasting. FreTS mainly involves two stages, (i) Domain Conversion, that transforms time-domain signals into complex numbers of frequency domain; (ii) Frequency Learning, that performs our redesigned MLPs for the learning of real and imaginary part of frequency components. The above stages operated on both inter-series and intra-series scales further contribute to channel-wise and time-wise dependency learning. Extensive experiments on 13 real-world benchmarks (including 7 benchmarks for short-term forecasting and 6 benchmarks for long-term forecasting) demonstrate our consistent superiority over state-of-the-art methods.

The widespread adoption of scalable mobile sensing has led to large amounts of time series data for real-world applications. A fundamental application is multivariate time series forecasting (MTSF), which aims to predict future time series values based on historical observations. Existing MTSF methods suffer from limited parameterization and small-scale training data. Recently, Large language models (LLMs) have been introduced in time series, which achieve promising forecasting performance but incur heavy computational costs. To solve these challenges, we propose TimeCMA, an LLM-empowered framework for time series forecasting with cross-modality alignment. We design a dual-modality encoding module with two branches, where the time series encoding branch extracts relatively low-quality yet pure embeddings of time series through an inverted Transformer. In addition, the LLM-empowered encoding branch wraps the same time series as prompts to obtain high-quality yet entangled prompt embeddings via a Pre-trained LLM. Then, we design a cross-modality alignment module to retrieve high-quality and pure time series embeddings from the prompt embeddings. Moreover, we develop a time series forecasting module to decode the aligned embeddings while capturing dependencies among multiple variables for forecasting. Notably, we tailor the prompt to encode sufficient temporal information into a last token and design the last token embedding storage to reduce computational costs. Extensive experiments on real data offer insight into the accuracy and efficiency of the proposed framework.

Learning time series foundation models has been shown to be a promising approach for zero-shot time series forecasting across diverse time series domains. Insofar as scaling has been a critical driver of performance of foundation models in other modalities such as language and vision, much recent work on time series foundation modeling has focused on scaling. This has resulted in time series foundation models with hundreds of millions of parameters that are, while performant, inefficient and expensive to use in practice. This paper describes a simple recipe for learning efficient foundation models for zero-shot time series forecasting that are orders of magnitude smaller. We show that large-scale transformers are not necessary: small hybrid models that interleave long convolution and linear RNN layers (in particular DeltaNet layers) can match the performance of larger transformer-based models while being more than a hundred times smaller. We also describe several data augmentation and inference strategies that further improve performance. This recipe results in Reverso, a family of efficient time series foundation models for zero-shot forecasting that significantly push the performance-efficiency Pareto frontier.

Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world small-sample scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progresses have been achieved as the emergence of large language models, exhibiting unprecedented ability in few-shot generalization, scalability, and task generality, which is however absent in time series models. To change the current practices of training small models on specific datasets from scratch, this paper aims at an early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), that is pre-trained by autoregressive next token prediction on large multi-domain datasets, and is fine-tuned to downstream scenarios with promising abilities as an LTSM.

Time Series Foundation Models (TSFMs) are transforming the field of forecasting. However, evaluating them on historical data is increasingly difficult due to the risks of train-test sample overlaps and temporal overlaps between correlated train and test time series. To address this, we introduce TS-Arena, a live forecasting platform that shifts evaluation from the known past to the unknown future. Building on the concept of continuous benchmarking, TS-Arena evaluates models on future data. Crucially, we introduce a strict forecasting pre-registration protocol: models must submit predictions before the ground-truth data physically exists. This makes test-set contamination impossible by design. The platform relies on a modular microservice architecture that harmonizes and structures data from different sources and orchestrates containerized model submissions. By enforcing a strict pre-registration protocol on live data streams, TS-Arena prevents information leakage offers a faster alternative to traditional static, infrequently repeated competitions (e.g. the M-Competitions). First empirical results derived from operating TS-Arena over one year of energy time series demonstrate that established TSFMs accumulate robust longitudinal scores over time, while the continuous nature of the benchmark simultaneously allows newcomers to demonstrate immediate competitiveness. TS-Arena provides the necessary infrastructure to assess the true generalization capabilities of modern forecasting models. The platform and corresponding code are available at https://ts-arena.live/.

Multivariate time series forecasting (MTSF) endeavors to predict future observations given historical data, playing a crucial role in time series data management systems. With advancements in large language models (LLMs), recent studies employ textual prompt tuning to infuse the knowledge of LLMs into MTSF. However, the deployment of LLMs often suffers from low efficiency during the inference phase. To address this problem, we introduce TimeKD, an efficient MTSF framework that leverages the calibrated language models and privileged knowledge distillation. TimeKD aims to generate high-quality future representations from the proposed cross-modality teacher model and cultivate an effective student model. The cross-modality teacher model adopts calibrated language models (CLMs) with ground truth prompts, motivated by the paradigm of Learning Under Privileged Information (LUPI). In addition, we design a subtractive cross attention (SCA) mechanism to refine these representations. To cultivate an effective student model, we propose an innovative privileged knowledge distillation (PKD) mechanism including correlation and feature distillation. PKD enables the student to replicate the teacher's behavior while minimizing their output discrepancy. Extensive experiments on real data offer insight into the effectiveness, efficiency, and scalability of the proposed TimeKD.

Recent work has shown that simple linear models can outperform several Transformer based approaches in long term time-series forecasting. Motivated by this, we propose a Multi-layer Perceptron (MLP) based encoder-decoder model, Time-series Dense Encoder (TiDE), for long-term time-series forecasting that enjoys the simplicity and speed of linear models while also being able to handle covariates and non-linear dependencies. Theoretically, we prove that the simplest linear analogue of our model can achieve near optimal error rate for linear dynamical systems (LDS) under some assumptions. Empirically, we show that our method can match or outperform prior approaches on popular long-term time-series forecasting benchmarks while being 5-10x faster than the best Transformer based model.

Time series foundation models (TSFMs) offer strong zero-shot forecasting via large-scale pre-training, yet fine-tuning remains critical for boosting performance in domains with limited public data. With the growing number of TSFMs, efficiently identifying the best model for downstream fine-tuning becomes increasingly challenging. In this work, we introduce TimeTic, a transferability estimation framework that recasts model selection as an in-context-learning problem: given observations on known (source) datasets, it predicts how a TSFM will perform after fine-tuning on a downstream (target) dataset. TimeTic flexibly organizes the observed model-data relationships as contextual information, allowing it to adapt seamlessly to various test-time scenarios. Leveraging the natural tabular structure formed by dataset meta-features, model characteristics, and fine-tuned performance, we employ tabular foundation models to serve as in-context learners. We further introduce a novel model characterization based on entropy evolution across model layers, capturing embedding-space distinctions and enabling TimeTic to generalize across arbitrary model sets. We establish a comprehensive benchmark for transferability estimation including 10 datasets, 10 foundation models, and 3 forecasting tasks. On this benchmark, TimeTic's estimation demonstrates strong alignment with actual fine-tuned performance for previously unseen datasets, achieving a mean rank correlation of approximately 0.6 and a 30% improvement compared to using zero-shot performance as the transferability score.

Time series analysis stands as a focal point within the data mining community, serving as a cornerstone for extracting valuable insights crucial to a myriad of real-world applications. Recent advances in Foundation Models (FMs) have fundamentally reshaped the paradigm of model design for time series analysis, boosting various downstream tasks in practice. These innovative approaches often leverage pre-trained or fine-tuned FMs to harness generalized knowledge tailored for time series analysis. This survey aims to furnish a comprehensive and up-to-date overview of FMs for time series analysis. While prior surveys have predominantly focused on either application or pipeline aspects of FMs in time series analysis, they have often lacked an in-depth understanding of the underlying mechanisms that elucidate why and how FMs benefit time series analysis. To address this gap, our survey adopts a methodology-centric classification, delineating various pivotal elements of time-series FMs, including model architectures, pre-training techniques, adaptation methods, and data modalities. Overall, this survey serves to consolidate the latest advancements in FMs pertinent to time series analysis, accentuating their theoretical underpinnings, recent strides in development, and avenues for future exploration.

Time Series Foundation Models (TSFMs) have shown significant impact through their model capacity, scalability, and zero-shot generalization. However, due to the heterogeneity of inter-variate dependencies and the backbone scalability on large-scale multivariate datasets, most TSFMs are typically pre-trained on univariate time series. This limitation renders them oblivious to crucial information from diverse covariates in real-world forecasting tasks. To further enhance the performance of TSFMs, we propose a general covariate-aware adaptation (CoRA) framework for TSFMs. It leverages pre-trained backbones of foundation models while effectively incorporating exogenous covariates from various modalities, including time series, language, and images, to improve the quality of predictions. Technically, CoRA maintains the equivalence of initialization and parameter consistency during adaptation. With preserved backbones of foundation models as frozen feature extractors, the outcome embeddings from foundation models are empirically demonstrated more informative than raw data. Further, CoRA employs a novel Granger Causality Embedding (GCE) to automatically evaluate covariates regarding their causal predictability with respect to the target variate. We incorporate these weighted embeddings with a zero-initialized condition-injection mechanism, avoiding catastrophic forgetting of pre-trained foundation models and gradually integrates exogenous information. Extensive experiments show that CoRA of TSFMs surpasses state-of-the-art covariate-aware deep forecasters with full or few-shot training samples, achieving 31.1% MSE reduction on covariate-aware forecasting. Compared to other adaptation methods, CoRA exhibits strong compatibility with various advanced TSFMs and extends the scope of covariates to other modalities, presenting a practical paradigm for the application of TSFMs.

Long-term forecasting presents unique challenges due to the time and memory complexity of handling long sequences. Existing methods, which rely on sliding windows to process long sequences, struggle to effectively capture long-term variations that are partially caught within the short window (i.e., outer-window variations). In this paper, we introduce a novel approach that overcomes this limitation by employing contrastive learning and enhanced decomposition architecture, specifically designed to focus on long-term variations. To this end, our contrastive loss incorporates global autocorrelation held in the whole time series, which facilitates the construction of positive and negative pairs in a self-supervised manner. When combined with our decomposition networks, our contrastive learning significantly improves long-term forecasting performance. Extensive experiments demonstrate that our approach outperforms 14 baseline models in multiple experiments over nine long-term benchmarks, especially in challenging scenarios that require a significantly long output for forecasting. Source code is available at https://github.com/junwoopark92/Self-Supervised-Contrastive-Forecsating.

Time series foundation models excel in zero-shot forecasting, handling diverse tasks without explicit training. However, the advancement of these models has been hindered by the lack of comprehensive benchmarks. To address this gap, we introduce the General Time Series Forecasting Model Evaluation, GIFT-Eval, a pioneering benchmark aimed at promoting evaluation across diverse datasets. GIFT-Eval encompasses 28 datasets over 144,000 time series and 177 million data points, spanning seven domains, 10 frequencies, multivariate inputs, and prediction lengths ranging from short to long-term forecasts. To facilitate the effective pretraining and evaluation of foundation models, we also provide a non-leaking pretraining dataset containing approximately 230 billion data points. Additionally, we provide a comprehensive analysis of 17 baselines, which includes statistical models, deep learning models, and foundation models. We discuss each model in the context of various benchmark characteristics and offer a qualitative analysis that spans both deep learning and foundation models. We believe the insights from this analysis, along with access to this new standard zero-shot time series forecasting benchmark, will guide future developments in time series foundation models. The codebase, datasets, and a leaderboard showing all the results in detail will be available soon.

The stock market is a fundamental component of financial systems, reflecting economic health, providing investment opportunities, and influencing global dynamics. Accurate stock market predictions can lead to significant gains and promote better investment decisions. However, predicting stock market trends is challenging due to their non-linear and stochastic nature. This study investigates the efficacy of advanced deep learning models for short-term trend forecasting using daily and hourly closing prices from the S&P 500 index and the Brazilian ETF EWZ. The models explored include Temporal Convolutional Networks (TCN), Neural Basis Expansion Analysis for Time Series Forecasting (N-BEATS), Temporal Fusion Transformers (TFT), Neural Hierarchical Interpolation for Time Series Forecasting (N-HiTS), and Time-series Dense Encoder (TiDE). Furthermore, we introduce the Extended Long Short-Term Memory for Time Series (xLSTM-TS) model, an xLSTM adaptation optimised for time series prediction. Wavelet denoising techniques were applied to smooth the signal and reduce minor fluctuations, providing cleaner data as input for all approaches. Denoising significantly improved performance in predicting stock price direction. Among the models tested, xLSTM-TS consistently outperformed others. For example, it achieved a test accuracy of 72.82% and an F1 score of 73.16% on the EWZ daily dataset. By leveraging advanced deep learning models and effective data preprocessing techniques, this research provides valuable insights into the application of machine learning for market movement forecasting, highlighting both the potential and the challenges involved.

Social and collaborative platforms emit multivariate time-series traces in which early interactions-such as views, likes, or downloads-are followed, sometimes months or years later, by higher impact like citations, sales, or reviews. We formalize this setting as Lead-Lag Forecasting (LLF): given an early usage channel (the lead), predict a correlated but temporally shifted outcome channel (the lag). Despite the ubiquity of such patterns, LLF has not been treated as a unified forecasting problem within the time-series community, largely due to the absence of standardized datasets. To anchor research in LLF, here we present two high-volume benchmark datasets-arXiv (accesses -> citations of 2.3M papers) and GitHub (pushes/stars -> forks of 3M repositories)-and outline additional domains with analogous lead-lag dynamics, including Wikipedia (page views -> edits), Spotify (streams -> concert attendance), e-commerce (click-throughs -> purchases), and LinkedIn profile (views -> messages). Our datasets provide ideal testbeds for lead-lag forecasting, by capturing long-horizon dynamics across years, spanning the full spectrum of outcomes, and avoiding survivorship bias in sampling. We documented all technical details of data curation and cleaning, verified the presence of lead-lag dynamics through statistical and classification tests, and benchmarked parametric and non-parametric baselines for regression. Our study establishes LLF as a novel forecasting paradigm and lays an empirical foundation for its systematic exploration in social and usage data. Our data portal with downloads and documentation is available at https://lead-lag-forecasting.github.io/.

In recent years, generative pre-trained paradigms such as Large Language Models (LLMs) and Large Vision Models (LVMs) have achieved revolutionary advancements and widespread real-world applications. Particularly, the emergence of pre-trained LLMs-based temporal works, compared to previous deep model approaches, has demonstrated superior generalization and robustness, showcasing the potential of generative pre-trained paradigms as foundation models for time series. However, those LLMs-based works mainly focus on cross-modal research, i.e., leveraging the language capabilities of LLMs in time series contexts. Although they have achieved impressive performance, there still exist the issues of concept drift caused by differences in data distribution and inflexibility caused by misalignment of dimensions. To this end, inspired by recent work on LVMs, we reconsider the paradigm of time series modeling. In this paper, we comprehensively explore, for the first time, the effectiveness and superiority of the Generative Pre-trained Diffusion (GPD) paradigm in real-world multivariate time series forecasting (TSF). Specifically, to mitigate performance bias introduced by sophisticated networks, we propose a straightforward MLP diffusion network for unconditional modeling of time series. Then we employ a zero-shot and tuning-free method to predict (generate) future data using historical data as prompts. The GPD paradigm is established on the time series modality, effectively preventing the phenomenon of concept drift, and enabling flexible forecasting of arbitrary lengths. We demonstrate that the GPD paradigm achieves comprehensive performance and generalization comparable to current SOTA LLM-based and deep model paradigms on mainstream benchmarks and various TSF tasks. Extensive experiments validate the potential of the GPD paradigm and its assistance in future related research.

We introduce the Cisco Time Series Model, a univariate zero-shot forecaster. This time series foundation model is the result of a general architectural innovation to a time series model enabling it to accept multiresolution input, applied to a popular decoder-only time series model (TimesFM). The resulting multiresolution decoder-only model is trained on over 300B unique data points, with more than half coming from the observability domain. Quantitative and qualitative evaluations demonstrate that the resulting model achieves superior performance on observability datasets while retaining very similar performance on a standard general-purpose forecasting benchmark (GIFT-Eval), and suggest that the multiresolution structure enables the model to make more accurate predictions on long context input.

Model selection is a critical step in time series forecasting, traditionally requiring extensive performance evaluations across various datasets. Meta-learning approaches aim to automate this process, but they typically depend on pre-constructed performance matrices, which are costly to build. In this work, we propose to leverage Large Language Models (LLMs) as a lightweight alternative for model selection. Our method eliminates the need for explicit performance matrices by utilizing the inherent knowledge and reasoning capabilities of LLMs. Through extensive experiments with LLaMA, GPT and Gemini, we demonstrate that our approach outperforms traditional meta-learning techniques and heuristic baselines, while significantly reducing computational overhead. These findings underscore the potential of LLMs in efficient model selection for time series forecasting.

We present Timer-XL, a generative Transformer for unified time series forecasting. To uniformly predict 1D and 2D time series, we generalize next token prediction, predominantly adopted for causal generation of 1D sequences, to multivariate next token prediction. The proposed paradigm uniformly formulates various forecasting scenarios as a long-context generation problem. We opt for the generative Transformer, which can capture global-range and causal dependencies while providing contextual flexibility, to implement unified forecasting on univariate series characterized by non-stationarity, multivariate time series with complicated dynamics and correlations, and covariate-informed contexts that include both endogenous and exogenous variables. Technically, we propose a universal TimeAttention to facilitate generative Transformers on time series, which can effectively capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches) and is further strengthened by position embeddings in both temporal and variable dimensions. Timer-XL achieves state-of-the-art performance across challenging forecasting benchmarks through a unified approach. As a large time series model, it demonstrates notable model transferability by large-scale pre-training, as well as contextual flexibility in token lengths, positioning it as a one-for-all forecaster.

Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algorithms over a wide variety of datasets. In this paper, we present such a comprehensive time series forecasting archive containing 20 publicly available time series datasets from varied domains, with different characteristics in terms of frequency, series lengths, and inclusion of missing values. We also characterise the datasets, and identify similarities and differences among them, by conducting a feature analysis. Furthermore, we present the performance of a set of standard baseline forecasting methods over all datasets across eight error metrics, for the benefit of researchers using the archive to benchmark their forecasting algorithms.

We introduce Timer-S1, a strong Mixture-of-Experts (MoE) time series foundation model with 8.3B total parameters, 0.75B activated parameters for each token, and a context length of 11.5K. To overcome the scalability bottleneck in existing pre-trained time series foundation models, we perform Serial Scaling in three dimensions: model architecture, dataset, and training pipeline. Timer-S1 integrates sparse TimeMoE blocks and generic TimeSTP blocks for Serial-Token Prediction (STP), a generic training objective that adheres to the serial nature of forecasting. The proposed paradigm introduces serial computations to improve long-term predictions while avoiding costly rolling-style inference and pronounced error accumulation in the standard next-token prediction. Pursuing a high-quality and unbiased training dataset, we curate TimeBench, a corpus with one trillion time points, and apply meticulous data augmentation to mitigate predictive bias. We further pioneer a post-training stage, including continued pre-training and long-context extension, to enhance short-term and long-context performance. Evaluated on the large-scale GIFT-Eval leaderboard, Timer-S1 achieves state-of-the-art forecasting performance, attaining the best MASE and CRPS scores as a pre-trained model. Timer-S1 will be released to facilitate further research.

In the realm of time series forecasting (TSF), it is imperative for models to adeptly discern and distill hidden patterns within historical time series data to forecast future states. Transformer-based models exhibit formidable efficacy in TSF, primarily attributed to their advantage in apprehending these patterns. However, the quadratic complexity of the Transformer leads to low computational efficiency and high costs, which somewhat hinders the deployment of the TSF model in real-world scenarios. Recently, Mamba, a selective state space model, has gained traction due to its ability to process dependencies in sequences while maintaining near-linear complexity. For TSF tasks, these characteristics enable Mamba to comprehend hidden patterns as the Transformer and reduce computational overhead compared to the Transformer. Therefore, we propose a Mamba-based model named Simple-Mamba (S-Mamba) for TSF. Specifically, we tokenize the time points of each variate autonomously via a linear layer. A bidirectional Mamba layer is utilized to extract inter-variate correlations and a Feed-Forward Network is set to learn temporal dependencies. Finally, the generation of forecast outcomes through a linear mapping layer. Experiments on thirteen public datasets prove that S-Mamba maintains low computational overhead and achieves leading performance. Furthermore, we conduct extensive experiments to explore Mamba's potential in TSF tasks. Our code is available at https://github.com/wzhwzhwzh0921/S-D-Mamba.

In this paper, we present a new approach to time series forecasting. Time series data are prevalent in many scientific and engineering disciplines. Time series forecasting is a crucial task in modeling time series data, and is an important area of machine learning. In this work we developed a novel method that employs Transformer-based machine learning models to forecast time series data. This approach works by leveraging self-attention mechanisms to learn complex patterns and dynamics from time series data. Moreover, it is a generic framework and can be applied to univariate and multivariate time series data, as well as time series embeddings. Using influenza-like illness (ILI) forecasting as a case study, we show that the forecasting results produced by our approach are favorably comparable to the state-of-the-art.

The success of large-scale pre-training paradigm, exemplified by Large Language Models (LLMs), has inspired the development of Time Series Foundation Models (TSFMs). However, their application to financial candlestick (K-line) data remains limited, often underperforming non-pre-trained architectures. Moreover, existing TSFMs often overlook crucial downstream tasks such as volatility prediction and synthetic data generation. To address these limitations, we propose Kronos, a unified, scalable pre-training framework tailored to financial K-line modeling. Kronos introduces a specialized tokenizer that discretizes continuous market information into token sequences, preserving both price dynamics and trade activity patterns. We pre-train Kronos using an autoregressive objective on a massive, multi-market corpus of over 12 billion K-line records from 45 global exchanges, enabling it to learn nuanced temporal and cross-asset representations. Kronos excels in a zero-shot setting across a diverse set of financial tasks. On benchmark datasets, Kronos boosts price series forecasting RankIC by 93% over the leading TSFM and 87% over the best non-pre-trained baseline. It also achieves a 9% lower MAE in volatility forecasting and a 22% improvement in generative fidelity for synthetic K-line sequences. These results establish Kronos as a robust, versatile foundation model for end-to-end financial time series analysis. Our pre-trained model is publicly available at https://github.com/shiyu-coder/Kronos.

Recent studies have indicated that vision models pre-trained on images can serve as time series foundation models (TSFMs) by reformulating time series forecasting (TSF) as image reconstruction. However, effective cross-modal transfer from vision to time series remains challenging due to three discrepancies: (1) the data-modality gap between structured, bounded image data and unbounded, heterogeneous time series; (2) the multivariate-forecasting gap between fixed RGB-three-channel vision models and time series with arbitrary numbers of variates; and (3) the probabilistic-forecasting gap between the deterministic outputs of vision models and the requirement for uncertainty-aware probabilistic predictions. To bridge these gaps, we propose VisonTS++, a TSFM based on continual pre-training of a vision model on large-scale time series. Our approach introduces three key innovations: (1) vision-model-based filtering to identify high-quality sequences to stabilize pre-training and mitigate modality gap; (2) colorized multivariate conversion, encoding multivariate series as multi-subfigure RGB images to enhance cross-variate modeling; (3) multi-quantile forecasting, using parallel reconstruction heads to generate quantile forecasts without parametric assumptions. Experiments show that VisionTS++ achieves state-of-the-art performance in both in-distribution and out-of-distribution forecasting, outperforming specialized TSFMs by 6%-44% in MSE reduction and ranking first in GIFT-Eval benchmark which comprises 23 datasets across 7 domains. Our work demonstrates that with appropriate adaptation, vision models can effectively generalize to TSF, thus advancing the pursuit of universal TSFMs. Code is available at https://github.com/HALF111/VisionTSpp.

Large pre-trained time series foundation models (TSFMs) have demonstrated promising zero-shot performance across a wide range of domains. However, a question remains: Do TSFMs succeed solely by memorizing training patterns, or do they possess the ability to reason? While reasoning is a topic of great interest in the study of Large Language Models (LLMs), it is undefined and largely unexplored in the context of TSFMs. In this work, inspired by language modeling literature, we formally define compositional reasoning in forecasting and distinguish it from in-distribution generalization. We evaluate the reasoning and generalization capabilities of 23 popular deep learning forecasting models on multiple synthetic and real-world datasets. Additionally, through controlled studies, we systematically examine which design choices in TSFMs contribute to improved reasoning abilities. Our study yields key insights into the impact of TSFM architecture design on compositional reasoning and generalization. We find that patch-based Transformers have the best reasoning performance, closely followed by residualized MLP-based architectures, which are 97\% less computationally complex in terms of FLOPs and 86\% smaller in terms of the number of trainable parameters. Interestingly, in some zero-shot out-of-distribution scenarios, these models can outperform moving average and exponential smoothing statistical baselines trained on in-distribution data. Only a few design choices, such as the tokenization method, had a significant (negative) impact on Transformer model performance.

Foundation models (FMs) have transformed natural language processing, but their success has not yet translated to time series forecasting. Existing time series foundation models (TSFMs), often based on transformer variants, struggle with generalization across varying context and target lengths, lack adaptability to different sampling rates, and are computationally inefficient. We introduce FlowState, a novel TSFM architecture that addresses these challenges through two key innovations: a state space model (SSM) based encoder and a functional basis decoder. This design enables continuous-time modeling and dynamic time-scale adjustment, allowing FlowState to inherently generalize across all possible temporal resolutions, and dynamically adjust the forecasting horizons. In contrast to other state-of-the-art TSFMs, which require training data across all possible sampling rates to memorize patterns at each scale, FlowState inherently adapts its internal dynamics to the input scale, enabling smaller models, reduced data requirements, and improved efficiency. We further propose an efficient pretraining strategy that improves robustness and accelerates training. Despite being the smallest model, FlowState outperforms all other models and is state-of-the-art for the GIFT-ZS and the Chronos-ZS benchmarks. Ablation studies confirm the effectiveness of its components, and we demonstrate its unique ability to adapt online to varying input sampling rates.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Foundation models for zero-shot time series forecasting face challenges in efficient long-horizon prediction and reproducibility, with existing synthetic-only approaches underperforming on challenging benchmarks. This paper presents TempoPFN, a univariate time series foundation model based on linear Recurrent Neural Networks (RNNs) pre-trained exclusively on synthetic data. The model uses a GatedDeltaProduct architecture with state-weaving for fully parallelizable training across sequence lengths, eliminating the need for windowing or summarization techniques while maintaining robust temporal state-tracking. Our comprehensive synthetic data pipeline unifies diverse generators, including stochastic differential equations, Gaussian processes, and audio synthesis, with novel augmentations. In zero-shot evaluations on the Gift-Eval benchmark, TempoPFN achieves top-tier competitive performance, outperforming all existing synthetic-only approaches and surpassing the vast majority of models trained on real-world data, while being more efficient than existing baselines by leveraging fully parallelizable training and inference. We open-source our complete data generation pipeline and training code, providing a reproducible foundation for future research.

In recent years, there has been increasing interest in developing foundation models for time series data that can generalize across diverse downstream tasks. While numerous forecasting-oriented foundation models have been introduced, there is a notable scarcity of models tailored for time series classification. To address this gap, we present Mantis, a new open-source foundation model for time series classification based on the Vision Transformer (ViT) architecture that has been pre-trained using a contrastive learning approach. Our experimental results show that Mantis outperforms existing foundation models both when the backbone is frozen and when fine-tuned, while achieving the lowest calibration error. In addition, we propose several adapters to handle the multivariate setting, reducing memory requirements and modeling channel interdependence.

Multivariate time series forecasting has seen widely ranging applications in various domains, including finance, traffic, energy, and healthcare. To capture the sophisticated temporal patterns, plenty of research studies designed complex neural network architectures based on many variants of RNNs, GNNs, and Transformers. However, complex models are often computationally expensive and thus face a severe challenge in training and inference efficiency when applied to large-scale real-world datasets. In this paper, we introduce LightTS, a light deep learning architecture merely based on simple MLP-based structures. The key idea of LightTS is to apply an MLP-based structure on top of two delicate down-sampling strategies, including interval sampling and continuous sampling, inspired by a crucial fact that down-sampling time series often preserves the majority of its information. We conduct extensive experiments on eight widely used benchmark datasets. Compared with the existing state-of-the-art methods, LightTS demonstrates better performance on five of them and comparable performance on the rest. Moreover, LightTS is highly efficient. It uses less than 5% FLOPS compared with previous SOTA methods on the largest benchmark dataset. In addition, LightTS is robust and has a much smaller variance in forecasting accuracy than previous SOTA methods in long sequence forecasting tasks.

Deep learning for time series forecasting has seen significant advancements over the past decades. However, despite the success of large-scale pre-training in language and vision domains, pre-trained time series models remain limited in scale and operate at a high cost, hindering the development of larger capable forecasting models in real-world applications. In response, we introduce Time-MoE, a scalable and unified architecture designed to pre-train larger, more capable forecasting foundation models while reducing inference costs. By leveraging a sparse mixture-of-experts (MoE) design, Time-MoE enhances computational efficiency by activating only a subset of networks for each prediction, reducing computational load while maintaining high model capacity. This allows Time-MoE to scale effectively without a corresponding increase in inference costs. Time-MoE comprises a family of decoder-only transformer models that operate in an auto-regressive manner and support flexible forecasting horizons with varying input context lengths. We pre-trained these models on our newly introduced large-scale data Time-300B, which spans over 9 domains and encompassing over 300 billion time points. For the first time, we scaled a time series foundation model up to 2.4 billion parameters, achieving significantly improved forecasting precision. Our results validate the applicability of scaling laws for training tokens and model size in the context of time series forecasting. Compared to dense models with the same number of activated parameters or equivalent computation budgets, our models consistently outperform them by large margin. These advancements position Time-MoE as a state-of-the-art solution for tackling real-world time series forecasting challenges with superior capability, efficiency, and flexibility.

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

Time-series forecasting in real-world applications such as finance and energy often faces challenges due to limited training data and complex, noisy temporal dynamics. Existing deep forecasting models typically supervise predictions using full-length temporal windows, which include substantial high-frequency noise and obscure long-term trends. Moreover, auxiliary variables containing rich domain-specific information are often underutilized, especially in few-shot settings. To address these challenges, we propose LoFT-LLM, a frequency-aware forecasting pipeline that integrates low-frequency learning with semantic calibration via a large language model (LLM). Firstly, a Patch Low-Frequency forecasting Module (PLFM) extracts stable low-frequency trends from localized spectral patches. Secondly, a residual learner then models high-frequency variations. Finally, a fine-tuned LLM refines the predictions by incorporating auxiliary context and domain knowledge through structured natural language prompts. Extensive experiments on financial and energy datasets demonstrate that LoFT-LLM significantly outperforms strong baselines under both full-data and few-shot regimes, delivering superior accuracy, robustness, and interpretability.

Time series forecasting is crucial for various applications, such as weather forecasting, power load forecasting, and financial analysis. In recent studies, MLP-mixer models for time series forecasting have been shown as a promising alternative to transformer-based models. However, the performance of these models is still yet to reach its potential. In this paper, we propose Wavelet Patch Mixer (WPMixer), a novel MLP-based model, for long-term time series forecasting, which leverages the benefits of patching, multi-resolution wavelet decomposition, and mixing. Our model is based on three key components: (i) multi-resolution wavelet decomposition, (ii) patching and embedding, and (iii) MLP mixing. Multi-resolution wavelet decomposition efficiently extracts information in both the frequency and time domains. Patching allows the model to capture an extended history with a look-back window and enhances capturing local information while MLP mixing incorporates global information. Our model significantly outperforms state-of-the-art MLP-based and transformer-based models for long-term time series forecasting in a computationally efficient way, demonstrating its efficacy and potential for practical applications.

Transformer-based foundation models have emerged as a dominant paradigm in time series analysis, offering unprecedented capabilities in tasks such as forecasting, anomaly detection, classification, trend analysis and many more time series analytical tasks. This survey provides a comprehensive overview of the current state of the art pre-trained foundation models, introducing a novel taxonomy to categorize them across several dimensions. Specifically, we classify models by their architecture design, distinguishing between those leveraging patch-based representations and those operating directly on raw sequences. The taxonomy further includes whether the models provide probabilistic or deterministic predictions, and whether they are designed to work with univariate time series or can handle multivariate time series out of the box. Additionally, the taxonomy encompasses model scale and complexity, highlighting differences between lightweight architectures and large-scale foundation models. A unique aspect of this survey is its categorization by the type of objective function employed during training phase. By synthesizing these perspectives, this survey serves as a resource for researchers and practitioners, providing insights into current trends and identifying promising directions for future research in transformer-based time series modeling.

Recent research on time-series foundation models (TSFMs) has underscored the scarcity of real-world data, often supplemented with synthetic sources in existing datasets, whose generalizability remains however debated. As such, in this work, we propose a novel benchmarking approach: in particular, we aim at building a curated dataset reflecting real world physical temporal dynamics, extracting temporal signals from real-world videos using optical flow. As such, we introduce REAL-V-TSFM, a novel dataset designed to capture rich and diverse time series derived from real-world videos. Experimental results on state-of-the-art TSFMs under zero-shot forecasting show that, despite strong performance on conventional benchmarks, these models exhibit performance degradation on the proposed dataset, suggesting limited generalizability to novel datasets. These findings underscore the need for novel approaches to acquiring time series data and highlight the lack of universality in recent TSFMs, while further validating the effectiveness of our video-based time series data extraction pipeline.

Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pretraining on large-scale, carefully curated collections of real-world sequences. To allow for a sample-efficient pretraining of TSFMs, we propose CauKer, a novel algorithm designed to generate diverse, causally coherent synthetic time series with realistic trends, seasonality, and nonlinear interactions. CauKer combines Gaussian Process (GP) kernel composition with Structural Causal Models (SCM) to produce data for sample-efficient pretraining of state-of-the-art classification TSFMs having different architectures and following different pretraining approaches. Additionally, our experiments reveal that CauKer-generated datasets exhibit clear scaling laws for both dataset size (10K to 10M samples) and model capacity (1M to 783M parameters), unlike real-world datasets, which display irregular scaling behavior.

Time series modeling presents unique challenges due to autocorrelation in both historical data and future sequences. While current research predominantly addresses autocorrelation within historical data, the correlations among future labels are often overlooked. Specifically, modern forecasting models primarily adhere to the Direct Forecast (DF) paradigm, generating multi-step forecasts independently and disregarding label autocorrelation over time. In this work, we demonstrate that the learning objective of DF is biased in the presence of label autocorrelation. To address this issue, we propose the Frequency-enhanced Direct Forecast (FreDF), which mitigates label autocorrelation by learning to forecast in the frequency domain, thereby reducing estimation bias. Our experiments show that FreDF significantly outperforms existing state-of-the-art methods and is compatible with a variety of forecast models. Code is available at https://github.com/Master-PLC/FreDF.

The success of large language models (LLMs) for time series has been demonstrated in previous work. Utilizing a symbolic time series representation, one can efficiently bridge the gap between LLMs and time series. However, the remaining challenge is to exploit the semantic information hidden in time series by using symbols or existing tokens of LLMs, while aligning the embedding space of LLMs according to the hidden information of time series. The symbolic time series approximation (STSA) method called adaptive Brownian bridge-based symbolic aggregation (ABBA) shows outstanding efficacy in preserving salient time series features by modeling time series patterns in terms of amplitude and period while using existing tokens of LLMs. In this paper, we introduce a method, called LLM-ABBA, that integrates ABBA into large language models for various downstream time series tasks. By symbolizing time series, LLM-ABBA compares favorably to the recent state-of-the-art (SOTA) in UCR and three medical time series classification tasks. Meanwhile, a fixed-polygonal chain trick in ABBA is introduced to avoid obvious drifting during forecasting tasks by significantly mitigating the effects of cumulative error arising from misused symbols during the transition from symbols to numerical values. In time series regression tasks, LLM-ABBA achieves the new SOTA on Time Series Extrinsic Regression (TSER) benchmarks. LLM-ABBA also shows competitive forecasting capability compared to recent SOTA time series forecasting results. We believe this framework can also seamlessly extend to other time series tasks. Our simulation code is publicly available at: https://github.com/inEXASCALE/llm-abba

Multivariate long-term and efficient time series forecasting is a key requirement for a variety of practical applications, and there are complex interleaving time dynamics in time series data that require decomposition modeling. Traditional time series decomposition methods are single and rely on fixed rules, which are insufficient for mining the potential information of the series and adapting to the dynamic characteristics of complex series. On the other hand, the Transformer-based models for time series forecasting struggle to effectively model long sequences and intricate dynamic relationships due to their high computational complexity. To overcome these limitations, we introduce KARMA, with an Adaptive Time Channel Decomposition module (ATCD) to dynamically extract trend and seasonal components. It further integrates a Hybrid Frequency-Time Decomposition module (HFTD) to further decompose Series into frequency-domain and time-domain. These components are coupled with multi-scale Mamba-based KarmaBlock to efficiently process global and local information in a coordinated manner. Experiments on eight real-world datasets from diverse domains well demonstrated that KARMA significantly outperforms mainstream baseline methods in both predictive accuracy and computational efficiency. Code and full results are available at this repository: https://github.com/yedadasd/KARMA

Time series data is fundamental to decision-making in many crucial domains including healthcare, finance, and environmental science. However, analyzing this data often requires incorporating unstructured contextual information, answering domain-specific questions, and generating natural language explanations -- capabilities that traditional time series models lack due to their inability to process text. While Large Language Models (LLMs) excel at contextual reasoning and knowledge integration, they struggle with numerical time series due to inefficient text-based representations and limited exposure to temporal data during pretraining. We address this gap by augmenting an LLM with specialized time series perception through a patch-based encoder-decoder architecture. We train this Time Series-augmented LLM (TsLLM) on a large corpus of over 2 million interleaved time series and text examples spanning diverse analysis tasks: forecasting with contextual information, time series question-answering, pattern explanation, classification with natural language outputs, and report generation. This training enables TsLLM to leverage both its language understanding and newly acquired temporal reasoning capabilities. While not designed to surpass specialized models on traditional benchmarks, TsLLM demonstrates strong performance on tasks requiring the integration of time series analysis with natural language -- capabilities that existing approaches cannot provide. Our work establishes a new paradigm for time series analysis that bridges numerical computation and natural language understanding, democratizing access to sophisticated temporal reasoning through natural language interaction.

This paper presents OLinear, a linear-based multivariate time series forecasting model that operates in an orthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we utilize OrthoTrans, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix. This approach enables more effective encoding and decoding in the decorrelated feature domain and can serve as a plug-in module to enhance existing forecasters. To enhance the representation learning for multivariate time series, we introduce a customized linear layer, NormLin, which employs a normalized weight matrix to capture multivariate dependencies. Empirically, the NormLin module shows a surprising performance advantage over multi-head self-attention, while requiring nearly half the FLOPs. Extensive experiments on 24 benchmarks and 140 forecasting tasks demonstrate that OLinear consistently achieves state-of-the-art performance with high efficiency. Notably, as a plug-in replacement for self-attention, the NormLin module consistently enhances Transformer-based forecasters. The code and datasets are available at https://anonymous.4open.science/r/OLinear

Foundation Models (FMs) have improved time series forecasting in various sectors, such as finance, but their vulnerability to input disturbances can hinder their adoption by stakeholders, such as investors and analysts. To address this, we propose a causally grounded rating framework to study the robustness of Foundational Models for Time Series (FMTS) with respect to input perturbations. We evaluate our approach to the stock price prediction problem, a well-studied problem with easily accessible public data, evaluating six state-of-the-art (some multi-modal) FMTS across six prominent stocks spanning three industries. The ratings proposed by our framework effectively assess the robustness of FMTS and also offer actionable insights for model selection and deployment. Within the scope of our study, we find that (1) multi-modal FMTS exhibit better robustness and accuracy compared to their uni-modal versions and, (2) FMTS pre-trained on time series forecasting task exhibit better robustness and forecasting accuracy compared to general-purpose FMTS pre-trained across diverse settings. Further, to validate our framework's usability, we conduct a user study showcasing FMTS prediction errors along with our computed ratings. The study confirmed that our ratings reduced the difficulty for users in comparing the robustness of different systems.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

Deep learning for time series forecasting has traditionally operated within a one-model-per-dataset framework, limiting its potential to leverage the game-changing impact of large pre-trained models. The concept of universal forecasting, emerging from pre-training on a vast collection of time series datasets, envisions a single Large Time Series Model capable of addressing diverse downstream forecasting tasks. However, constructing such a model poses unique challenges specific to time series data: i) cross-frequency learning, ii) accommodating an arbitrary number of variates for multivariate time series, and iii) addressing the varying distributional properties inherent in large-scale data. To address these challenges, we present novel enhancements to the conventional time series Transformer architecture, resulting in our proposed Masked Encoder-based Universal Time Series Forecasting Transformer (Moirai). Trained on our newly introduced Large-scale Open Time Series Archive (LOTSA) featuring over 27B observations across nine domains, Moirai achieves competitive or superior performance as a zero-shot forecaster when compared to full-shot models. Code, model weights, and data will be released.

Time series forecasting always faces the challenge of concept drift, where data distributions evolve over time, leading to a decline in forecast model performance. Existing solutions are based on online learning, which continually organize recent time series observations as new training samples and update model parameters according to the forecasting feedback on recent data. However, they overlook a critical issue: obtaining ground-truth future values of each sample should be delayed until after the forecast horizon. This delay creates a temporal gap between the training samples and the test sample. Our empirical analysis reveals that the gap can introduce concept drift, causing forecast models to adapt to outdated concepts. In this paper, we present Proceed, a novel proactive model adaptation framework for online time series forecasting. Proceed first estimates the concept drift between the recently used training samples and the current test sample. It then employs an adaptation generator to efficiently translate the estimated drift into parameter adjustments, proactively adapting the model to the test sample. To enhance the generalization capability of the framework, Proceed is trained on synthetic diverse concept drifts. Extensive experiments on five real-world datasets across various forecast models demonstrate that Proceed brings more performance improvements than the state-of-the-art online learning methods, significantly facilitating forecast models' resilience against concept drifts. Code is available at https://github.com/SJTU-DMTai/OnlineTSF.

We introduce TFRBench, the first benchmark designed to evaluate the reasoning capabilities of forecasting systems. Traditionally, time-series forecasting has been evaluated solely on numerical accuracy, treating foundation models as ``black boxes.'' Unlike existing benchmarks, TFRBench provides a protocol for evaluating the reasoning generated by forecasting systems--specifically their analysis of cross-channel dependencies, trends, and external events. To enable this, we propose a systematic multi-agent framework that utilizes an iterative verification loop to synthesize numerically grounded reasoning traces. Spanning ten datasets across five domains, our evaluation confirms that this reasoning is causally effective; useful for evaluation; and prompting LLMs with our generated traces significantly improves forecasting accuracy compared to direct numerical prediction (e.g., avg. sim40.2%to56.6%), validating the quality of our reasoning. Conversely, benchmarking experiments reveal that off-the-shelf LLMs consistently struggle with both reasoning (lower LLM-as-a-Judge scores) and numerical forecasting, frequently failing to capture domain-specific dynamics. TFRBench thus establishes a new standard for interpretable, reasoning-based evaluation in time-series forecasting. Our benchmark is available at: https://tfrbench.github.io

In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities. We introduce TiRex that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state-tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM. TiRex sets a new state of the art in zero-shot time series forecasting on the HuggingFace benchmarks GiftEval and Chronos-ZS, outperforming significantly larger models including TabPFN-TS (Prior Labs), Chronos Bolt (Amazon), TimesFM (Google), and Moirai (Salesforce) across both short- and long-term forecasts.

Forecasting time series data is a critical area of research with applications spanning from stock prices to early epidemic prediction. While numerous statistical and machine learning methods have been proposed, real-life prediction problems often require hybrid solutions that bridge classical forecasting approaches and modern neural network models. In this study, we introduce the Probabilistic AutoRegressive Neural Networks (PARNN), capable of handling complex time series data exhibiting non-stationarity, nonlinearity, non-seasonality, long-range dependence, and chaotic patterns. PARNN is constructed by improving autoregressive neural networks (ARNN) using autoregressive integrated moving average (ARIMA) feedback error, combining the explainability, scalability, and "white-box-like" prediction behavior of both models. Notably, the PARNN model provides uncertainty quantification through prediction intervals, setting it apart from advanced deep learning tools. Through comprehensive computational experiments, we evaluate the performance of PARNN against standard statistical, machine learning, and deep learning models, including Transformers, NBeats, and DeepAR. Diverse real-world datasets from macroeconomics, tourism, epidemiology, and other domains are employed for short-term, medium-term, and long-term forecasting evaluations. Our results demonstrate the superiority of PARNN across various forecast horizons, surpassing the state-of-the-art forecasters. The proposed PARNN model offers a valuable hybrid solution for accurate long-range forecasting. By effectively capturing the complexities present in time series data, it outperforms existing methods in terms of accuracy and reliability. The ability to quantify uncertainty through prediction intervals further enhances the model's usefulness in decision-making processes.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

Recent advances in Large Language Models (LLMs) have demonstrated new possibilities for accurate and efficient time series analysis, but prior work often required heavy fine-tuning and/or ignored inter-series correlations. In this work, we explore simple and flexible prompt-based strategies that enable LLMs to perform time series forecasting without extensive retraining or the use of a complex external architecture. Through the exploration of specialized prompting methods that leverage time series decomposition, patch-based tokenization, and similarity-based neighbor augmentation, we find that it is possible to enhance LLM forecasting quality while maintaining simplicity and requiring minimal preprocessing of data. To this end, we propose our own method, PatchInstruct, which enables LLMs to make precise and effective predictions.

Recent efforts have been dedicated to enhancing time series forecasting accuracy by introducing advanced network architectures and self-supervised pretraining strategies. Nevertheless, existing approaches still exhibit two critical drawbacks. Firstly, these methods often rely on a single dataset for training, limiting the model's generalizability due to the restricted scale of the training data. Secondly, the one-step generation schema is widely followed, which necessitates a customized forecasting head and overlooks the temporal dependencies in the output series, and also leads to increased training costs under different horizon length settings. To address these issues, we propose a novel generative pretrained hierarchical transformer architecture for forecasting, named GPHT. There are two aspects of key designs in GPHT. On the one hand, we advocate for constructing a mixed dataset for pretraining our model, comprising various datasets from diverse data scenarios. This approach significantly expands the scale of training data, allowing our model to uncover commonalities in time series data and facilitating improved transfer to specific datasets. On the other hand, GPHT employs an auto-regressive forecasting approach under the channel-independent assumption, effectively modeling temporal dependencies in the output series. Importantly, no customized forecasting head is required, enabling a single model to forecast at arbitrary horizon settings. We conduct sufficient experiments on eight datasets with mainstream self-supervised pretraining models and supervised models. The results demonstrated that GPHT surpasses the baseline models across various fine-tuning and zero/few-shot learning settings in the traditional long-term forecasting task, providing support for verifying the feasibility of pretrained time series large models.

Data augmentation is important for improving machine learning model performance when faced with limited real-world data. In time series forecasting (TSF), where accurate predictions are crucial in fields like finance, healthcare, and manufacturing, traditional augmentation methods for classification tasks are insufficient to maintain temporal coherence. This research introduces two augmentation approaches using the discrete wavelet transform (DWT) to adjust frequency elements while preserving temporal dependencies in time series data. Our methods, Wavelet Masking (WaveMask) and Wavelet Mixing (WaveMix), are evaluated against established baselines across various forecasting horizons. To the best of our knowledge, this is the first study to conduct extensive experiments on multivariate time series using Discrete Wavelet Transform as an augmentation technique. Experimental results demonstrate that our techniques achieve competitive results with previous methods. We also explore cold-start forecasting using downsampled training datasets, comparing outcomes to baseline methods.

Time series forecasting plays a vital role in supporting decision-making across a wide range of critical applications, including energy, healthcare, and finance. Despite recent advances, forecasting accuracy remains limited due to the challenge of integrating historical numerical sequences with contextual features, which often comprise unstructured textual data. To address this challenge, we propose TokenCast, an LLM-driven framework that leverages language-based symbolic representations as a unified intermediary for context-aware time series forecasting. Specifically, TokenCast employs a discrete tokenizer to transform continuous numerical sequences into temporal tokens, enabling structural alignment with language-based inputs. To bridge the semantic gap between modalities, both temporal and contextual tokens are embedded into a shared representation space via a pre-trained large language model (LLM), further optimized with autoregressive generative objectives. Building upon this unified semantic space, the aligned LLM is subsequently fine-tuned in a supervised manner to predict future temporal tokens, which are then decoded back into the original numerical space. Extensive experiments on diverse real-world datasets enriched with contextual features demonstrate the effectiveness and generalizability of TokenCast.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

Forecasting multiple future events within a given time horizon is essential for applications in finance, retail, social networks, and healthcare. Marked Temporal Point Processes (MTPP) provide a principled framework to model both the timing and labels of events. However, most existing research focuses on predicting only the next event, leaving long-horizon forecasting largely underexplored. To address this gap, we introduce HoTPP, the first benchmark specifically designed to rigorously evaluate long-horizon predictions. We identify shortcomings in widely used evaluation metrics, propose a theoretically grounded T-mAP metric, present strong statistical baselines, and offer efficient implementations of popular models. Our empirical results demonstrate that modern MTPP approaches often underperform simple statistical baselines. Furthermore, we analyze the diversity of predicted sequences and find that most methods exhibit mode collapse. Finally, we analyze the impact of autoregression and intensity-based losses on prediction quality, and outline promising directions for future research. The HoTPP source code, hyperparameters, and full evaluation results are available at GitHub.

Predictive model design for accurately predicting future stock prices has always been considered an interesting and challenging research problem. The task becomes complex due to the volatile and stochastic nature of the stock prices in the real world which is affected by numerous controllable and uncontrollable variables. This paper presents an optimized predictive model built on long-and-short-term memory (LSTM) architecture for automatically extracting past stock prices from the web over a specified time interval and predicting their future prices for a specified forecast horizon, and forecasts the future stock prices. The model is deployed for making buy and sell transactions based on its predicted results for 70 important stocks from seven different sectors listed in the National Stock Exchange (NSE) of India. The profitability of each sector is derived based on the total profit yielded by the stocks in that sector over a period from Jan 1, 2010 to Aug 26, 2021. The sectors are compared based on their profitability values. The prediction accuracy of the model is also evaluated for each sector. The results indicate that the model is highly accurate in predicting future stock prices.

Data augmentation (DA) has become a de facto solution to expand training data size for deep learning. With the proliferation of deep models for time series analysis, various time series DA techniques are proposed in the literature, e.g., cropping-, warping-, flipping-, and mixup-based methods. However, these augmentation methods mainly apply to time series classification and anomaly detection tasks. In time series forecasting (TSF), we need to model the fine-grained temporal relationship within time series segments to generate accurate forecasting results given data in a look-back window. Existing DA solutions in the time domain would break such a relationship, leading to poor forecasting accuracy. To tackle this problem, this paper proposes simple yet effective frequency domain augmentation techniques that ensure the semantic consistency of augmented data-label pairs in forecasting, named FrAug. We conduct extensive experiments on eight widely-used benchmarks with several state-of-the-art TSF deep models. Our results show that FrAug can boost the forecasting accuracy of TSF models in most cases. Moreover, we show that FrAug enables models trained with 1\% of the original training data to achieve similar performance to the ones trained on full training data, which is particularly attractive for cold-start forecasting. Finally, we show that applying test-time training with FrAug greatly improves forecasting accuracy for time series with significant distribution shifts, which often occurs in real-life TSF applications. Our code is available at https://anonymous.4open.science/r/Fraug-more-results-1785.

Real-world multivariate time series can exhibit intricate multi-scale structures, including global trends, local periodicities, and non-stationary regimes, which makes long-horizon forecasting challenging. Although sparse Mixture-of-Experts (MoE) approaches improve scalability and specialization, they typically rely on homogeneous MLP experts that poorly capture the diverse temporal dynamics of time series data. We address these limitations with MoHETS, an encoder-only Transformer that integrates sparse Mixture-of-Heterogeneous-Experts (MoHE) layers. MoHE routes temporal patches to a small subset of expert networks, combining a shared depthwise-convolution expert for sequence-level continuity with routed Fourier-based experts for patch-level periodic structures. MoHETS further improves robustness to non-stationary dynamics by incorporating exogenous information via cross-attention over covariate patch embeddings. Finally, we replace parameter-heavy linear projection heads with a lightweight convolutional patch decoder, improving parameter efficiency, reducing training instability, and allowing a single model to generalize across arbitrary forecast horizons. We validate across seven multivariate benchmarks and multiple horizons, with MoHETS consistently achieving state-of-the-art performance, reducing the average MSE by 12% compared to strong recent baselines, demonstrating effective heterogeneous specialization for long-term forecasting.

We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies diffusion-based probabilistic regression methods. Within this framework, FALDA leverages Fourier-based decomposition to incorporate a component-specific architecture, enabling tailored modeling of individual temporal components. A conditional diffusion model is utilized to estimate the future noise term, while our proposed lightweight denoiser, DEMA (Decomposition MLP with AdaLN), conditions on the historical noise term to enhance denoising performance. Through mathematical analysis and empirical validation, we demonstrate that FALDA effectively reduces epistemic uncertainty, allowing probabilistic learning to primarily focus on aleatoric uncertainty. Experiments on six real-world benchmarks demonstrate that FALDA consistently outperforms existing probabilistic forecasting approaches across most datasets for long-term time series forecasting while achieving enhanced computational efficiency without compromising accuracy. Notably, FALDA also achieves superior overall performance compared to state-of-the-art (SOTA) point forecasting approaches, with improvements of up to 9%.

Transformers have been actively studied for time-series forecasting in recent years. While often showing promising results in various scenarios, traditional Transformers are not designed to fully exploit the characteristics of time-series data and thus suffer some fundamental limitations, e.g., they generally lack of decomposition capability and interpretability, and are neither effective nor efficient for long-term forecasting. In this paper, we propose ETSFormer, a novel time-series Transformer architecture, which exploits the principle of exponential smoothing in improving Transformers for time-series forecasting. In particular, inspired by the classical exponential smoothing methods in time-series forecasting, we propose the novel exponential smoothing attention (ESA) and frequency attention (FA) to replace the self-attention mechanism in vanilla Transformers, thus improving both accuracy and efficiency. Based on these, we redesign the Transformer architecture with modular decomposition blocks such that it can learn to decompose the time-series data into interpretable time-series components such as level, growth and seasonality. Extensive experiments on various time-series benchmarks validate the efficacy and advantages of the proposed method. Code is available at https://github.com/salesforce/ETSformer.

This work summarizes two strategies for completing time-series (TS) tasks using today's language model (LLM): LLM-for-TS, design and train a fundamental large model for TS data; TS-for-LLM, enable the pre-trained LLM to handle TS data. Considering the insufficient data accumulation, limited resources, and semantic context requirements, this work focuses on TS-for-LLM methods, where we aim to activate LLM's ability for TS data by designing a TS embedding method suitable for LLM. The proposed method is named TEST. It first tokenizes TS, builds an encoder to embed them by instance-wise, feature-wise, and text-prototype-aligned contrast, and then creates prompts to make LLM more open to embeddings, and finally implements TS tasks. Experiments are carried out on TS classification and forecasting tasks using 8 LLMs with different structures and sizes. Although its results cannot significantly outperform the current SOTA models customized for TS tasks, by treating LLM as the pattern machine, it can endow LLM's ability to process TS data without compromising the language ability. This paper is intended to serve as a foundational work that will inspire further research.

We present TimeFound, an encoder-decoder transformer-based time series foundation model for out-of-the-box zero-shot forecasting. To handle time series data from various domains, TimeFound employs a multi-resolution patching strategy to capture complex temporal patterns at multiple scales. We pre-train our model with two sizes (200M and 710M parameters) on a large time-series corpus comprising both real-world and synthetic datasets. Over a collection of unseen datasets across diverse domains and forecasting horizons, our empirical evaluations suggest that TimeFound can achieve superior or competitive zero-shot forecasting performance, compared to state-of-the-art time series foundation models.

Due to the recurrent structure of RNN, the long information propagation path poses limitations in capturing long-term dependencies, gradient explosion/vanishing issues, and inefficient sequential execution. Based on this, we propose a novel paradigm called Parallel Gated Network (PGN) as the new successor to RNN. PGN directly captures information from previous time steps through the designed Historical Information Extraction (HIE) layer and leverages gated mechanisms to select and fuse it with the current time step information. This reduces the information propagation path to O(1), effectively addressing the limitations of RNN. To enhance PGN's performance in long-range time series forecasting tasks, we propose a novel temporal modeling framework called Temporal PGN (TPGN). TPGN incorporates two branches to comprehensively capture the semantic information of time series. One branch utilizes PGN to capture long-term periodic patterns while preserving their local characteristics. The other branch employs patches to capture short-term information and aggregate the global representation of the series. TPGN achieves a theoretical complexity of O(L), ensuring efficiency in its operations. Experimental results on five benchmark datasets demonstrate the state-of-the-art (SOTA) performance and high efficiency of TPGN, further confirming the effectiveness of PGN as the new successor to RNN in long-range time series forecasting. The code is available in this repository: https://github.com/Water2sea/TPGN.

With the volatile and complex nature of financial data influenced by external factors, forecasting the stock market is challenging. Traditional models such as ARIMA and GARCH perform well with linear data but struggle with non-linear dependencies. Machine learning and deep learning models, particularly Long Short-Term Memory (LSTM) networks, address these challenges by capturing intricate patterns and long-term dependencies. This report compares ARIMA and LSTM models in predicting the S&P 500 index, a major financial benchmark. Using historical price data and technical indicators, we evaluated these models using Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). The ARIMA model showed reasonable performance with an MAE of 462.1, RMSE of 614, and 89.8 percent accuracy, effectively capturing short-term trends but limited by its linear assumptions. The LSTM model, leveraging sequential processing capabilities, outperformed ARIMA with an MAE of 369.32, RMSE of 412.84, and 92.46 percent accuracy, capturing both short- and long-term dependencies. Notably, the LSTM model without additional features performed best, achieving an MAE of 175.9, RMSE of 207.34, and 96.41 percent accuracy, showcasing its ability to handle market data efficiently. Accurately predicting stock movements is crucial for investment strategies, risk assessments, and market stability. Our findings confirm the potential of deep learning models in handling volatile financial data compared to traditional ones. The results highlight the effectiveness of LSTM and suggest avenues for further improvements. This study provides insights into financial forecasting, offering a comparative analysis of ARIMA and LSTM while outlining their strengths and limitations.

In recent years, deep learning techniques have outperformed traditional models in many machine learning tasks. Deep neural networks have successfully been applied to address time series forecasting problems, which is a very important topic in data mining. They have proved to be an effective solution given their capacity to automatically learn the temporal dependencies present in time series. However, selecting the most convenient type of deep neural network and its parametrization is a complex task that requires considerable expertise. Therefore, there is a need for deeper studies on the suitability of all existing architectures for different forecasting tasks. In this work, we face two main challenges: a comprehensive review of the latest works using deep learning for time series forecasting; and an experimental study comparing the performance of the most popular architectures. The comparison involves a thorough analysis of seven types of deep learning models in terms of accuracy and efficiency. We evaluate the rankings and distribution of results obtained with the proposed models under many different architecture configurations and training hyperparameters. The datasets used comprise more than 50000 time series divided into 12 different forecasting problems. By training more than 38000 models on these data, we provide the most extensive deep learning study for time series forecasting. Among all studied models, the results show that long short-term memory (LSTM) and convolutional networks (CNN) are the best alternatives, with LSTMs obtaining the most accurate forecasts. CNNs achieve comparable performance with less variability of results under different parameter configurations, while also being more efficient.

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local temporal dynamics and the decoding heterogeneity of forecasting. Such designs lose details in information-dense regions, introduce redundancy in stable segments, and fail to capture the distinct complexities of short-term and long-term horizons. We propose TimeMosaic, a forecasting framework that aims to address temporal heterogeneity. TimeMosaic employs adaptive patch embedding to dynamically adjust granularity according to local information density, balancing motif reuse with structural clarity while preserving temporal continuity. In addition, it introduces segment-wise decoding that treats each prediction horizon as a related subtask and adapts to horizon-specific difficulty and information requirements, rather than applying a single uniform decoder. Extensive evaluations on benchmark datasets demonstrate that TimeMosaic delivers consistent improvements over existing methods, and our model trained on the large-scale corpus with 321 billion observations achieves performance competitive with state-of-the-art TSFMs.

Accurate electricity load forecasting is essential for grid stability, resource optimization, and renewable energy integration. While transformer-based deep learning models like TimeGPT have gained traction in time-series forecasting, their effectiveness in long-term electricity load prediction remains uncertain. This study evaluates forecasting models ranging from classical regression techniques to advanced deep learning architectures using data from the ESD 2025 competition. The dataset includes two years of historical electricity load data, alongside temperature and global horizontal irradiance (GHI) across five sites, with a one-day-ahead forecasting horizon. Since actual test set load values remain undisclosed, leveraging predicted values would accumulate errors, making this a long-term forecasting challenge. We employ (i) Principal Component Analysis (PCA) for dimensionality reduction and (ii) frame the task as a regression problem, using temperature and GHI as covariates to predict load for each hour, (iii) ultimately stacking 24 models to generate yearly forecasts. Our results reveal that deep learning models, including TimeGPT, fail to consistently outperform simpler statistical and machine learning approaches due to the limited availability of training data and exogenous variables. In contrast, XGBoost, with minimal feature engineering, delivers the lowest error rates across all test cases while maintaining computational efficiency. This highlights the limitations of deep learning in long-term electricity forecasting and reinforces the importance of model selection based on dataset characteristics rather than complexity. Our study provides insights into practical forecasting applications and contributes to the ongoing discussion on the trade-offs between traditional and modern forecasting methods.

Time series forecasting is important across various domains for decision-making. In particular, financial time series such as stock prices can be hard to predict as it is difficult to model short-term and long-term temporal dependencies between data points. Convolutional Neural Networks (CNN) are good at capturing local patterns for modeling short-term dependencies. However, CNNs cannot learn long-term dependencies due to the limited receptive field. Transformers on the other hand are capable of learning global context and long-term dependencies. In this paper, we propose to harness the power of CNNs and Transformers to model both short-term and long-term dependencies within a time series, and forecast if the price would go up, down or remain the same (flat) in the future. In our experiments, we demonstrated the success of the proposed method in comparison to commonly adopted statistical and deep learning methods on forecasting intraday stock price change of S&P 500 constituents.

We introduce AutoGluon-TimeSeries - an open-source AutoML library for probabilistic time series forecasting. Focused on ease of use and robustness, AutoGluon-TimeSeries enables users to generate accurate point and quantile forecasts with just 3 lines of Python code. Built on the design philosophy of AutoGluon, AutoGluon-TimeSeries leverages ensembles of diverse forecasting models to deliver high accuracy within a short training time. AutoGluon-TimeSeries combines both conventional statistical models, machine-learning based forecasting approaches, and ensembling techniques. In our evaluation on 29 benchmark datasets, AutoGluon-TimeSeries demonstrates strong empirical performance, outperforming a range of forecasting methods in terms of both point and quantile forecast accuracy, and often even improving upon the best-in-hindsight combination of prior methods.

Recent innovations in transformers have shown their superior performance in natural language processing (NLP) and computer vision (CV). The ability to capture long-range dependencies and interactions in sequential data has also triggered a great interest in time series modeling, leading to the widespread use of transformers in many time series applications. However, being the most common and crucial application, the adaptation of transformers to time series forecasting has remained limited, with both promising and inconsistent results. In contrast to the challenges in NLP and CV, time series problems not only add the complexity of order or temporal dependence among input sequences but also consider trend, level, and seasonality information that much of this data is valuable for decision making. The conventional training scheme has shown deficiencies regarding model overfitting, data scarcity, and privacy issues when working with transformers for a forecasting task. In this work, we propose attentive federated transformers for time series stock forecasting with better performance while preserving the privacy of participating enterprises. Empirical results on various stock data from the Yahoo! Finance website indicate the superiority of our proposed scheme in dealing with the above challenges and data heterogeneity in federated learning.

In this paper, we introduce TimeGPT, the first foundation model for time series, capable of generating accurate predictions for diverse datasets not seen during training. We evaluate our pre-trained model against established statistical, machine learning, and deep learning methods, demonstrating that TimeGPT zero-shot inference excels in performance, efficiency, and simplicity. Our study provides compelling evidence that insights from other domains of artificial intelligence can be effectively applied to time series analysis. We conclude that large-scale time series models offer an exciting opportunity to democratize access to precise predictions and reduce uncertainty by leveraging the capabilities of contemporary advancements in deep learning.

While large language models have rapidly evolved towards general artificial intelligence, their versatility in analyzing time series data remains limited. To address this limitation, we propose a novel normalization technique that considers the inherent nature of tokenization. The proposed Tokenization-Optimized Normalization (TOKON) simplifies time series data by representing each element with a single token, effectively reducing the number of tokens by 2 to 3 times. Additionally, we introduce a novel prompt for time series forecasting, termed Time Series Forecasting with Care (TFSC), to further enhance forecasting performance. Experimental results demonstrate that TOKON improves root mean square error (RMSE) for multi-step forecasting by approximately 7% to 18%, depending on the dataset and prompting method. Furthermore, TFSC, when used in conjunction with TOKON, shows additional improvements in forecasting accuracy for certain datasets

Forecasting is a critical task in decision-making across numerous domains. While historical numerical data provide a start, they fail to convey the complete context for reliable and accurate predictions. Human forecasters frequently rely on additional information, such as background knowledge and constraints, which can efficiently be communicated through natural language. However, in spite of recent progress with LLM-based forecasters, their ability to effectively integrate this textual information remains an open question. To address this, we introduce "Context is Key" (CiK), a time-series forecasting benchmark that pairs numerical data with diverse types of carefully crafted textual context, requiring models to integrate both modalities; crucially, every task in CiK requires understanding textual context to be solved successfully. We evaluate a range of approaches, including statistical models, time series foundation models, and LLM-based forecasters, and propose a simple yet effective LLM prompting method that outperforms all other tested methods on our benchmark. Our experiments highlight the importance of incorporating contextual information, demonstrate surprising performance when using LLM-based forecasting models, and also reveal some of their critical shortcomings. This benchmark aims to advance multimodal forecasting by promoting models that are both accurate and accessible to decision-makers with varied technical expertise. The benchmark can be visualized at https://servicenow.github.io/context-is-key-forecasting/v0/.

The scientific reasoning ability of large language models (LLMs) has recently attracted significant attention. Time series, as a fundamental modality in scientific data, presents unique challenges that are often overlooked in current multimodal LLMs, which either encode numerical sequences as text or convert them into images. Such approaches may be insufficient for comprehensive scientific time series understanding and generation. Existing unified time series models typically specialise in either forecasting or analysis, and their effectiveness on non-periodic, heterogeneous scientific signals remains unclear. To address these gaps, we introduce SciTS, a benchmark spanning 12 scientific domains and 43 tasks, with over 50k+ instances, both univariate and multivariate signals ranging from 10^0 to 10^7 in length and up to 10~MHz in frequency. We benchmark 17 models, including text-only LLMs, multimodal LLMs, and unified time series models, and find that general-purpose LLMs exhibit stronger generalisability than specialised time series models, while representing time series as text or images limits their performance due to excessively long sequences and loss of numerical precision, respectively. We then introduce TimeOmni, a framework that equips LLMs with the ability to understand and generate time series while remaining compatible with general-purpose LLM training. This work fills a gap in both dedicated benchmarks and modelling frameworks for scientific time series, paving the way for LLMs to understand and generate complex temporal scientific data.

This paper introduces Mamba4Cast, a zero-shot foundation model for time series forecasting. Based on the Mamba architecture and inspired by Prior-data Fitted Networks (PFNs), Mamba4Cast generalizes robustly across diverse time series tasks without the need for dataset specific fine-tuning. Mamba4Cast's key innovation lies in its ability to achieve strong zero-shot performance on real-world datasets while having much lower inference times than time series foundation models based on the transformer architecture. Trained solely on synthetic data, the model generates forecasts for entire horizons in a single pass, outpacing traditional auto-regressive approaches. Our experiments show that Mamba4Cast performs competitively against other state-of-the-art foundation models in various data sets while scaling significantly better with the prediction length. The source code can be accessed at https://github.com/automl/Mamba4Cast.

Large Language Models (LLMs) offer the potential for automatic time series analysis and reporting, which is a critical task across many domains, spanning healthcare, finance, climate, energy, and many more. In this paper, we propose a framework for rigorously evaluating the capabilities of LLMs on time series understanding, encompassing both univariate and multivariate forms. We introduce a comprehensive taxonomy of time series features, a critical framework that delineates various characteristics inherent in time series data. Leveraging this taxonomy, we have systematically designed and synthesized a diverse dataset of time series, embodying the different outlined features. This dataset acts as a solid foundation for assessing the proficiency of LLMs in comprehending time series. Our experiments shed light on the strengths and limitations of state-of-the-art LLMs in time series understanding, revealing which features these models readily comprehend effectively and where they falter. In addition, we uncover the sensitivity of LLMs to factors including the formatting of the data, the position of points queried within a series and the overall time series length.

Recent research on time series foundation models has primarily focused on forecasting, leaving it unclear how generalizable their learned representations are. In this study, we examine whether frozen pre-trained forecasting models can provide effective representations for classification. To this end, we compare different representation extraction strategies and introduce two model-agnostic embedding augmentations. Our experiments show that the best forecasting models achieve classification accuracy that matches or even surpasses that of state-of-the-art models pre-trained specifically for classification. Moreover, we observe a positive correlation between forecasting and classification performance. These findings challenge the assumption that task-specific pre-training is necessary, and suggest that learning to forecast may provide a powerful route toward constructing general-purpose time series foundation models.