Scalable Transformer for High Dimensional Multivariate Time Series Forecasting

Abstract: Deep models for Multivariate Time Series (MTS) forecasting have recently demonstrated significant success. Channel-dependent models capture complex dependencies that channel-independent models cannot capture. However, the number of channels in real-world applications outpaces the capabilities of existing channel-dependent models, and contrary to common expectations, some models underperform the channel-independent models in handling high-dimensional data, which raises questions about the performance of channel-dependent models. To address this, our study first investigates the reasons behind the suboptimal performance of these channel-dependent models on high-dimensional MTS data. Our analysis reveals that two primary issues lie in the introduced noise from unrelated series that increases the difficulty of capturing the crucial inter-channel dependencies, and challenges in training strategies due to high-dimensional data. To address these issues, we propose STHD, the Scalable Transformer for High-Dimensional Multivariate Time Series Forecasting. STHD has three components: a) Relation Matrix Sparsity that limits the noise introduced and alleviates the memory issue; b) ReIndex applied as a training strategy to enable a more flexible batch size setting and increase the diversity of training data; and c) Transformer that handles 2-D inputs and captures channel dependencies. These components jointly enable STHD to manage the high-dimensional MTS while maintaining computational feasibility. Furthermore, experimental results show STHD's considerable improvement on three high-dimensional datasets: Crime-Chicago, Wiki-People, and Traffic. The source code and dataset are publicly available https://github.com/xinzzzhou/ScalableTransformer4HighDimensionMTSF.git.

Xin Zhou
Weiqing Wang
Wray Buntine
Shilin Qu
Abishek Sriramulu
Weicong Tan
Christoph Bergmeir

International Conference on Information and Knowledge Management


Inter-Series Transformer: Attending to Products in Time Series Forecasting

Abstract: Time series forecasting is an important task in many fields ranging from supply chain management to weather forecasting. Recently, Transformer neural network architectures have shown promising results in forecasting on common time series benchmark datasets. However, application to supply chain demand forecasting, which can have challenging characteristics such as sparsity and cross-series effects, has been limited. In this work, we explore the application of Transformer-based models to supply chain demand forecasting. In particular, we develop a new Transformer-based forecasting approach using a shared, multi-task per-time series network with an initial component applying attention across time series, to capture interactions and help address sparsity. We provide a case study applying our approach to successfully improve demand prediction for a medical device manufacturing company. To further validate our approach, we also apply it to public demand forecasting datasets as well and demonstrate competitive to superior performance compared to a variety of baseline and state-of-the-art forecast methods across the private and public datasets.

Rares Cristian
Pavithra Harsha
Clemente Ocejo
Georgia Perakis
Brian Quanz
Ioannis Spantidakis
Hamza Zerhouni


Time series forecasting with high stakes: A field study of the air cargo industry

Abstract: Time series forecasting in the air cargo industry presents unique challenges due to volatile market dynamics and the significant impact of accurate forecasts on generated revenue. This paper explores a comprehensive approach to demand forecasting at the origin-destination (O\&D) level, focusing on the development and implementation of machine learning models in decision-making for the air cargo industry. We leverage a mixture of experts framework, combining statistical and advanced deep learning models to provide reliable forecasts for cargo demand over a six-month horizon. The results demonstrate that our approach outperforms industry benchmarks, offering actionable insights for cargo capacity allocation and strategic decision-making in the air cargo industry. While this work is applied in the airline industry, the methodology is broadly applicable to any field where forecast-based decision-making in a volatile environment is crucial.

Abhinav Garg
Naman Shukla
Maarten Wormer


Survey and Taxonomy: The Role of Data-Centric AI in Transformer-Based Time Series Forecasting

Abstract: Alongside the continuous process of improving AI performance through the development of more sophisticated models, researchers have also focused their attention to the emerging concept of data-centric AI, which emphasizes the important role of data in a systematic machine learning training process. Nonetheless, the development of models has also continued apace. One result of this progress is the development of the Transformer Architecture, which possesses a high level of capability in multiple domains such as Natural Language Processing (NLP), Computer Vision (CV) and Time Series Forecasting (TSF). Its performance is, however, heavily dependent on input data preprocessing and output data evaluation, justifying a data-centric approach to future research. We argue that data-centric AI is essential for training AI models, particularly for transformer-based TSF models efficiently. However, there is a gap regarding the integration of transformer-based TSF and data-centric AI. This survey aims to pin down this gap via the extensive literature review based on the proposed taxonomy. We review the previous research works from a data-centric AI perspective and we intend to lay the foundation work for the future development of transformer-based architecture and data-centric AI.

Jingjing Xu
Caesar Wu
Yuan-Fang Li
Gregoire Danoy
Pascal Bouvry


DAM: Towards A Foundation Model for Time Series Forecasting

Abstract: It is challenging to scale time series forecasting models such that they forecast accurately for multiple distinct domains and datasets, all with potentially different underlying collection procedures (e.g., sample resolution), patterns (e.g., periodicity), and prediction requirements (e.g., reconstruction vs. forecasting). We call this general task universal forecasting. Existing methods usually assume that input data is regularly sampled, and they forecast to pre-determined horizons, resulting in failure to generalise outside of the scope of their training. We propose the DAM - a neural model that takes randomly sampled histories and outputs an adjustable basis composition as a continuous function of time for forecasting to non-fixed horizons. It involves three key components: (1) a flexible approach for using randomly sampled histories from a long-tail distribution, that enables an efficient global perspective of the underlying temporal dynamics while retaining focus on the recent history; (2) a transformer backbone that is trained on these actively sampled histories to produce, as representational output, (3) the basis coefficients of a continuous function of time. We show that a single univariate DAM, trained on 25 time series datasets, either outperformed or closely matched existing SoTA models at multivariate long-term forecasting across 18 datasets, including 8 held-out for zero-shot transfer, even though these models were trained to specialise for each dataset-horizon combination. This single DAM excels at zero-shot transfer and very-long-term forecasting, performs well at imputation, is interpretable via basis function composition and attention, can be tuned for different inference-cost requirements, is robust to missing and irregularly sampled data {by design}.

Luke Darlow
Qiwen Deng
Ahmed Hassan
Martin Asenov
Rajkarn Singh
Artjom Joosen
Adam Barker
Amos Storkey


On the optimal prediction of extreme events in heavy-tailed time series with applications to solar flare forecasting

Abstract: The prediction of extreme events in time series is a fundamental problem arising in many financial, scientific, engineering, and other applications. We begin by establishing a general Neyman-Pearson-type characterization of optimal extreme event predictors in terms of density ratios. This yields new insights and several closed-form optimal extreme event predictors for additive models. These results naturally extend to time series, where we study optimal extreme event prediction for both light- and heavy-tailed autoregressive and moving average models. Using a uniform law of large numbers for ergodic time series, we establish the asymptotic optimality of an empirical version of the optimal predictor for autoregressive models. Using multivariate regular variation, we obtain an expression for the optimal extremal precision in heavy-tailed infinite moving averages, which provides theoretical bounds on the ability to predict extremes in this general class of models. We address the important problem of predicting solar flares by applying our theory and methodology to a state-of-the-art time series consisting of solar soft X-ray flux measurements. Our results demonstrate the success and limitations in solar flare forecasting of long-memory autoregressive models and long-range-dependent, heavy-tailed FARIMA models.


ViTime: Foundation Model for Time Series Forecasting Powered by Vision Intelligence

Abstract: Time series forecasting (TSF) possesses great practical values in various fields, including power and energy, transportation, etc. TSF methods have been studied based on knowledge from classical statistics to modern deep learning. Yet, all of them were developed based on one fundamental concept, the numerical data fitting. Thus, the models developed have long been known to be problem-specific and lacking application generalizability. Practitioners expect a TSF foundation model that serves TSF tasks in different applications. The central question is then how to develop such a TSF foundation model. This paper offers one pioneering study in the TSF foundation model development method and proposes a vision intelligence-powered framework, ViTime, for the first time. ViTime fundamentally shifts TSF from numerical fitting to operations based on a binary image-based time series metric space and naturally supports both point and probabilistic forecasting. We also provide rigorous theoretical analyses of ViTime, including quantization-induced system error bounds and principled strategies for optimal parameter selection. Furthermore, we propose RealTS, an innovative synthesis algorithm generating diverse and realistic training samples, effectively enriching the training data and significantly enhancing model generalizability. Extensive experiments demonstrate ViTime's state-of-the-art performance. In zero-shot scenarios, ViTime outperforms TimesFM by 9-15\%. With just 10\% fine-tuning data, ViTime surpasses both leading foundation models and fully-supervised benchmarks, a gap that widens with 100\% fine-tuning. ViTime also exhibits exceptional robustness, effectively handling missing data and outperforming TimesFM by 20-30\% under various data perturbations, validating the power of its visual space data operation paradigm.

Luoxiao Yang
Yun Wang
Xinqi Fan
Israel Cohen
Jingdong Chen
Zijun Zhang

Transactions on Machine Learning Research,2025


Toto: Time Series Optimized Transformer for Observability

Abstract: This technical report describes the Time Series Optimized Transformer for Observability (Toto), a new state of the art foundation model for time series forecasting developed by Datadog. In addition to advancing the state of the art on generalized time series benchmarks in domains such as electricity and weather, this model is the first general-purpose time series forecasting foundation model to be specifically tuned for observability metrics. Toto was trained on a dataset of one trillion time series data points, the largest among all currently published time series foundation models. Alongside publicly available time series datasets, 75% of the data used to train Toto consists of fully anonymous numerical metric data points from the Datadog platform. In our experiments, Toto outperforms existing time series foundation models on observability data. It does this while also excelling at general-purpose forecasting tasks, achieving state-of-the-art zero-shot performance on multiple open benchmark datasets.

Ben Cohen
Emaad Khwaja
Kan Wang
Charles Masson
Elise Ramé
Youssef Doubli
Othmane Abou-Amal


JANET: Joint Adaptive predictioN-region Estimation for Time-series

Abstract: Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (Joint Adaptive predictioN-region Estimation for Time-series), a novel framework for constructing conformal prediction regions that are valid for both univariate and multivariate time series. JANET generalises the inductive conformal framework and efficiently produces joint prediction regions with controlled K-familywise error rates, enabling flexible adaptation to specific application needs. Our empirical evaluation demonstrates JANET's superior performance in multi-step prediction tasks across diverse time series datasets, highlighting its potential for reliable and interpretable uncertainty quantification in sequential data.

Eshant English
Eliot Wong-Toi
Matteo Fontana
Stephan Mandt
Padhraic Smyth
Christoph Lippert


On the Workflows and Smells of Leaderboard Operations (LBOps): An Exploratory Study of Foundation Model Leaderboards

Abstract: Foundation models (FM), such as large language models (LLMs), which are large-scale machine learning (ML) models, have demonstrated remarkable adaptability in various downstream software engineering (SE) tasks, such as code completion, code understanding, and software development. As a result, FM leaderboards have become essential tools for SE teams to compare and select the best third-party FMs for their specific products and purposes. However, the lack of standardized guidelines for FM evaluation and comparison threatens the transparency of FM leaderboards and limits stakeholders' ability to perform effective FM selection. As a first step towards addressing this challenge, our research focuses on understanding how these FM leaderboards operate in real-world scenarios ("leaderboard operations") and identifying potential pitfalls and areas for improvement ("leaderboard smells"). In this regard, we collect up to 1,045 FM leaderboards from five different sources: GitHub, Hugging Face Spaces, Papers With Code, spreadsheet and independent platform, to examine their documentation and engage in direct communication with leaderboard operators to understand their workflows. Through card sorting and negotiated agreement, we identify five distinct workflow patterns and develop a domain model that captures the key components and their interactions within these workflows. We then identify eight unique types of leaderboard smells in LBOps. By mitigating these smells, SE teams can improve transparency, accountability, and collaboration in current LBOps practices, fostering a more robust and responsible ecosystem for FM comparison and selection.

Zhimin Zhao
Abdul Ali Bangash
Filipe Roseiro Côgo
Bram Adams
Ahmed E. Hassan

IEEE Transactions on Software Engineering


Are Language Models Actually Useful for Time Series Forecasting?

Abstract: Large language models (LLMs) are being applied to time series forecasting. But are language models actually useful for time series? In a series of ablation studies on three recent and popular LLM-based time series forecasting methods, we find that removing the LLM component or replacing it with a basic attention layer does not degrade forecasting performance -- in most cases, the results even improve! We also find that despite their significant computational cost, pretrained LLMs do no better than models trained from scratch, do not represent the sequential dependencies in time series, and do not assist in few-shot settings. Additionally, we explore time series encoders and find that patching and attention structures perform similarly to LLM-based forecasters.

Mingtian Tan
Mike A. Merrill
Vinayak Gupta
Tim Althoff
Thomas Hartvigsen


WindowMixer: Intra-Window and Inter-Window Modeling for Time Series Forecasting

Abstract: Time series forecasting (TSF) is crucial in fields like economic forecasting, weather prediction, traffic flow analysis, and public health surveillance. Real-world time series data often include noise, outliers, and missing values, making accurate forecasting challenging. Traditional methods model point-to-point relationships, which limits their ability to capture complex temporal patterns and increases their susceptibility to noise.To address these issues, we introduce the WindowMixer model, built on an all-MLP framework. WindowMixer leverages the continuous nature of time series by examining temporal variations from a window-based perspective. It decomposes time series into trend and seasonal components, handling them individually. For trends, a fully connected (FC) layer makes predictions. For seasonal components, time windows are projected to produce window tokens, processed by Intra-Window-Mixer and Inter-Window-Mixer modules. The Intra-Window-Mixer models relationships within each window, while the Inter-Window-Mixer models relationships between windows. This approach captures intricate patterns and long-range dependencies in the data.Experiments show WindowMixer consistently outperforms existing methods in both long-term and short-term forecasting tasks.

Quangao Liu
Ruiqi Li
Maowei Jiang
Wei Yang
Chen Liang
LongLong Pang
Zhuozhang Zou


Fredformer: Frequency Debiased Transformer for Time Series Forecasting

Abstract: The Transformer model has shown leading performance in time series forecasting. Nevertheless, in some complex scenarios, it tends to learn low-frequency features in the data and overlook high-frequency features, showing a frequency bias. This bias prevents the model from accurately capturing important high-frequency data features. In this paper, we undertook empirical analyses to understand this bias and discovered that frequency bias results from the model disproportionately focusing on frequency features with higher energy. Based on our analysis, we formulate this bias and propose Fredformer, a Transformer-based framework designed to mitigate frequency bias by learning features equally across different frequency bands. This approach prevents the model from overlooking lower amplitude features important for accurate forecasting. Extensive experiments show the effectiveness of our proposed approach, which can outperform other baselines in different real-world time-series datasets. Furthermore, we introduce a lightweight variant of the Fredformer with an attention matrix approximation, which achieves comparable performance but with much fewer parameters and lower computation costs. The code is available at: https://github.com/chenzRG/Fredformer

Xihao Piao
Zheng Chen
Taichi Murayama
Yasuko Matsubara
Yasushi Sakurai


Time Series Analysis: yesterday, today, tomorrow

Abstract: Forecasts of various processes have always been a sophisticated problem for statistics and data science. Over the past decades the solution procedures were updated by deep learning and kernel methods. According to many specialists, these approaches are much more precise, stable, and suitable compared to the classical statistical linear time series methods. Here we investigate how true this point of view is.


Data Augmentation for Multivariate Time Series Classification: An Experimental Study

Abstract: Our study investigates the impact of data augmentation on the performance of multivariate time series models, focusing on datasets from the UCR archive. Despite the limited size of these datasets, we achieved classification accuracy improvements in 10 out of 13 datasets using the Rocket and InceptionTime models. This highlights the essential role of sufficient data in training effective models, paralleling the advancements seen in computer vision. Our work delves into adapting and applying existing methods in innovative ways to the domain of multivariate time series classification. Our comprehensive exploration of these techniques sets a new standard for addressing data scarcity in time series analysis, emphasizing that diverse augmentation strategies are crucial for unlocking the potential of both traditional and deep learning models. Moreover, by meticulously analyzing and applying a variety of augmentation techniques, we demonstrate that strategic data enrichment can enhance model accuracy. This not only establishes a benchmark for future research in time series analysis but also underscores the importance of adopting varied augmentation approaches to improve model performance in the face of limited data availability.

Romain Ilbert
Thai V. Hoang
Zonghua Zhang


UniTST: Effectively Modeling Inter-Series and Intra-Series Dependencies for Multivariate Time Series Forecasting

Abstract: Transformer-based models have emerged as powerful tools for multivariate time series forecasting (MTSF). However, existing Transformer models often fall short of capturing both intricate dependencies across variate and temporal dimensions in MTS data. Some recent models are proposed to separately capture variate and temporal dependencies through either two sequential or parallel attention mechanisms. However, these methods cannot directly and explicitly learn the intricate inter-series and intra-series dependencies. In this work, we first demonstrate that these dependencies are very important as they usually exist in real-world data. To directly model these dependencies, we propose a transformer-based model UniTST containing a unified attention mechanism on the flattened patch tokens. Additionally, we add a dispatcher module which reduces the complexity and makes the model feasible for a potentially large number of variates. Although our proposed model employs a simple architecture, it offers compelling performance as shown in our extensive experiments on several datasets for time series forecasting.

Juncheng Liu
Chenghao Liu
Gerald Woo
Yiwei Wang
Bryan Hooi
Caiming Xiong
Doyen Sahoo


FPN-fusion: Enhanced Linear Complexity Time Series Forecasting Model

Abstract: This study presents a novel time series prediction model, FPN-fusion, designed with linear computational complexity, demonstrating superior predictive performance compared to DLiner without increasing parameter count or computational demands. Our model introduces two key innovations: first, a Feature Pyramid Network (FPN) is employed to effectively capture time series data characteristics, bypassing the traditional decomposition into trend and seasonal components. Second, a multi-level fusion structure is developed to integrate deep and shallow features seamlessly. Empirically, FPN-fusion outperforms DLiner in 31 out of 32 test cases on eight open-source datasets, with an average reduction of 16.8% in mean squared error (MSE) and 11.8% in mean absolute error (MAE). Additionally, compared to the transformer-based PatchTST, FPN-fusion achieves 10 best MSE and 15 best MAE results, using only 8% of PatchTST's total computational load in the 32 test projects.


Time-Series Foundation Models for Forecasting Soil Moisture Levels in Smart Agriculture

Abstract: The recent surge in foundation models for natural language processing and computer vision has fueled innovation across various domains. Inspired by this progress, we explore the potential of foundation models for time-series forecasting in smart agriculture, a field often plagued by limited data availability. Specifically, this work presents a novel application of $\texttt{TimeGPT}$, a state-of-the-art (SOTA) time-series foundation model, to predict soil water potential ($ψ_\mathrm{soil}$), a key indicator of field water status that is typically used for irrigation advice. Traditionally, this task relies on a wide array of input variables. We explore $ψ_\mathrm{soil}$'s ability to forecast $ψ_\mathrm{soil}$ in: ($i$) a zero-shot setting, ($ii$) a fine-tuned setting relying solely on historic $ψ_\mathrm{soil}$ measurements, and ($iii$) a fine-tuned setting where we also add exogenous variables to the model. We compare $\texttt{TimeGPT}$'s performance to established SOTA baseline models for forecasting $ψ_\mathrm{soil}$. Our results demonstrate that $\texttt{TimeGPT}$ achieves competitive forecasting accuracy using only historical $ψ_\mathrm{soil}$ data, highlighting its remarkable potential for agricultural applications. This research paves the way for foundation time-series models for sustainable development in agriculture by enabling forecasting tasks that were traditionally reliant on extensive data collection and domain expertise.

Boje Deforce
Bart Baesens
Estefanía Serral Asensio


Are Self-Attentions Effective for Time Series Forecasting?

Abstract: Time series forecasting is crucial for applications across multiple domains and various scenarios. Although Transformer models have dramatically advanced the landscape of forecasting, their effectiveness remains debated. Recent findings have indicated that simpler linear models might outperform complex Transformer-based approaches, highlighting the potential for more streamlined architectures. In this paper, we shift the focus from evaluating the overall Transformer architecture to specifically examining the effectiveness of self-attention for time series forecasting. To this end, we introduce a new architecture, Cross-Attention-only Time Series transformer (CATS), that rethinks the traditional Transformer framework by eliminating self-attention and leveraging cross-attention mechanisms instead. By establishing future horizon-dependent parameters as queries and enhanced parameter sharing, our model not only improves long-term forecasting accuracy but also reduces the number of parameters and memory usage. Extensive experiment across various datasets demonstrates that our model achieves superior performance with the lowest mean squared error and uses fewer parameters compared to existing models. The implementation of our model is available at: https://github.com/dongbeank/CATS.

Dongbin Kim
Jinseong Park
Jaewook Lee
Hoki Kim


Dominant Shuffle: A Simple Yet Powerful Data Augmentation for Time-series Prediction

Abstract: Recent studies have suggested frequency-domain Data augmentation (DA) is effec tive for time series prediction. Existing frequency-domain augmentations disturb the original data with various full-spectrum noises, leading to excess domain gap between augmented and original data. Although impressive performance has been achieved in certain cases, frequency-domain DA has yet to be generalized to time series prediction datasets. In this paper, we found that frequency-domain augmentations can be significantly improved by two modifications that limit the perturbations. First, we found that limiting the perturbation to only dominant frequencies significantly outperforms full-spectrum perturbations. Dominant fre quencies represent the main periodicity and trends of the signal and are more important than other frequencies. Second, we found that simply shuffling the dominant frequency components is superior over sophisticated designed random perturbations. Shuffle rearranges the original components (magnitudes and phases) and limits the external noise. With these two modifications, we proposed dominant shuffle, a simple yet effective data augmentation for time series prediction. Our method is very simple yet powerful and can be implemented with just a few lines of code. Extensive experiments with eight datasets and six popular time series models demonstrate that our method consistently improves the baseline performance under various settings and significantly outperforms other DA methods. Code can be accessed at https://kaizhao.net/time-series.


Scaling Law for Time Series Forecasting

Abstract: Scaling law that rewards large datasets, complex models and enhanced data granularity has been observed in various fields of deep learning. Yet, studies on time series forecasting have cast doubt on scaling behaviors of deep learning methods for time series forecasting: while more training data improves performance, more capable models do not always outperform less capable models, and longer input horizons may hurt performance for some models. We propose a theory for scaling law for time series forecasting that can explain these seemingly abnormal behaviors. We take into account the impact of dataset size and model complexity, as well as time series data granularity, particularly focusing on the look-back horizon, an aspect that has been unexplored in previous theories. Furthermore, we empirically evaluate various models using a diverse set of time series forecasting datasets, which (1) verifies the validity of scaling law on dataset size and model complexity within the realm of time series forecasting, and (2) validates our theoretical framework, particularly regarding the influence of look back horizon. We hope our findings may inspire new models targeting time series forecasting datasets of limited size, as well as large foundational datasets and models for time series forecasting in future work. Code for our experiments has been made public at https://github.com/JingzheShi/ScalingLawForTimeSeriesForecasting.


Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer

Abstract: With the growing availability of multi-domain time series data, there is an increasing demand for general forecasting models pre-trained on multi-source datasets to support diverse downstream prediction scenarios. Existing time series foundation models primarily focus on scaling up pre-training datasets and model sizes to enhance generalization performance. In this paper, we take a different approach by addressing two critical aspects of general forecasting models: (1) how to derive unified representations from heterogeneous multi-domain time series data, and (2) how to effectively capture domain-specific features to enable adaptive transfer across various downstream scenarios. To address the first aspect, we propose Decomposed Frequency Learning as the pre-training task, which leverages frequency-based masking and reconstruction to decompose coupled semantic information in time series, resulting in unified representations across domains. For the second aspect, we introduce the Time Series Register, which captures domain-specific representations during pre-training and enhances adaptive transferability to downstream tasks. Our model achieves the state-of-the-art forecasting performance on seven real-world benchmarks, demonstrating remarkable few-shot and zero-shot capabilities.

Yihang Wang
Yuying Qiu
Peng Chen
Kai Zhao
Yang Shu
Zhongwen Rao
Lujia Pan
Bin Yang
Chenjuan Guo

International Conference on Machine Learning


Time-FFM: Towards LM-Empowered Federated Foundation Model for Time Series Forecasting

Abstract: Unlike natural language processing and computer vision, the development of Foundation Models (FMs) for time series forecasting is blocked due to data scarcity. While recent efforts are focused on building such FMs by unlocking the potential of language models (LMs) for time series analysis, dedicated parameters for various downstream forecasting tasks need training, which hinders the common knowledge sharing across domains. Moreover, data owners may hesitate to share the access to local data due to privacy concerns and copyright protection, which makes it impossible to simply construct a FM on cross-domain training instances. To address these issues, we propose Time-FFM, a Federated Foundation Model for Time series forecasting by leveraging pretrained LMs. Specifically, we begin by transforming time series into the modality of text tokens. To bootstrap LMs for time series reasoning, we propose a prompt adaption module to determine domain-customized prompts dynamically instead of artificially. Given the data heterogeneity across domains, we design a personalized federated training strategy by learning global encoders and local prediction heads. Our comprehensive experiments indicate that Time-FFM outperforms state-of-the-arts and promises effective few-shot and zero-shot forecaster.

Qingxiang Liu
Xu Liu
Chenghao Liu
Qingsong Wen
Yuxuan Liang


Scaling-laws for Large Time-series Models

Abstract: Scaling laws for large language models (LLMs) have provided useful guidance in training ever larger models for predictable performance gains. Time series forecasting shares a similar sequential structure to language, and is amenable to large-scale transformer architectures. Here we show that foundational decoder-only time series transformer models exhibit analogous scaling-behavior to LLMs, with architectural details (aspect ratio and number of heads) having a minimal effect over broad ranges. We assemble a large corpus of heterogenous time series data on which to train, and establish for the first time power-law scaling with parameter count, dataset size, and training compute, spanning five orders of magnitude.

Thomas D. P. Edwards
James Alvey
Justin Alsing
Nam H. Nguyen
Benjamin D. Wandelt


Interpretable Multivariate Time Series Forecasting Using Neural Fourier Transform

Abstract: Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines multi-dimensional Fourier transforms with Temporal Convolutional Network layers to improve both the accuracy and interpretability of forecasts. The Neural Fourier Transform is empirically validated on fourteen diverse datasets, showing superior performance across multiple forecasting horizons and lookbacks, setting new benchmarks in the field. This work advances multivariate time series forecasting by providing a model that is both interpretable and highly predictive, making it a valuable tool for both practitioners and researchers. The code for this study is publicly available.


Leveraging 2D Information for Long-term Time Series Forecasting with Vanilla Transformers

Abstract: Time series prediction is crucial for understanding and forecasting complex dynamics in various domains, ranging from finance and economics to climate and healthcare. Based on Transformer architecture, one approach involves encoding multiple variables from the same timestamp into a single temporal token to model global dependencies. In contrast, another approach embeds the time points of individual series into separate variate tokens. The former method faces challenges in learning variate-centric representations, while the latter risks missing essential temporal information critical for accurate forecasting. In our work, we introduce GridTST, a model that combines the benefits of two approaches using innovative multi-directional attentions based on a vanilla Transformer. We regard the input time series data as a grid, where the $x$-axis represents the time steps and the $y$-axis represents the variates. A vertical slicing of this grid combines the variates at each time step into a \textit{time token}, while a horizontal slicing embeds the individual series across all time steps into a \textit{variate token}. Correspondingly, a \textit{horizontal attention mechanism} focuses on time tokens to comprehend the correlations between data at various time steps, while a \textit{vertical}, variate-aware \textit{attention} is employed to grasp multivariate correlations. This combination enables efficient processing of information across both time and variate dimensions, thereby enhancing the model's analytical strength. % We also integrate the patch technique, segmenting time tokens into subseries-level patches, ensuring that local semantic information is retained in the embedding. The GridTST model consistently delivers state-of-the-art performance across various real-world datasets.

Xin Cheng
Xiuying Chen
Shuqi Li
Di Luo
Xun Wang
Dongyan Zhao
Rui Yan


Enhancing Transformer-based models for Long Sequence Time Series Forecasting via Structured Matrix

Abstract: Recently, Transformer-based models for long sequence time series forecasting have demonstrated promising results. The self-attention mechanism as the core component of these Transformer-based models exhibits great potential in capturing various dependencies among data points. Despite these advancements, it has been a subject of concern to improve the efficiency of the self-attention mechanism. Unfortunately, current specific optimization methods are facing the challenges in applicability and scalability for the future design of long sequence time series forecasting models. Hence, in this article, we propose a novel architectural framework that enhances Transformer-based models through the integration of Surrogate Attention Blocks (SAB) and Surrogate Feed-Forward Neural Network Blocks (SFB). The framework reduces both time and space complexity by the replacement of the self-attention and feed-forward layers with SAB and SFB while maintaining their expressive power and architectural advantages. The equivalence of this substitution is fully demonstrated. The extensive experiments on 10 Transformer-based models across five distinct time series tasks demonstrate an average performance improvement of 12.4%, alongside 61.3% reduction in parameter counts.

Zhicheng Zhang
Yong Wang
Shaoqi Tan
Bowei Xia
Yujie Luo


Low-Rank Adaptation of Time Series Foundational Models for Out-of-Domain Modality Forecasting

Abstract: Low-Rank Adaptation (LoRA) is a widely used technique for fine-tuning large pre-trained or foundational models across different modalities and tasks. However, its application to time series data, particularly within foundational models, remains underexplored. This paper examines the impact of LoRA on contemporary time series foundational models: Lag-Llama, MOIRAI, and Chronos. We demonstrate LoRA's fine-tuning potential for forecasting the vital signs of sepsis patients in intensive care units (ICUs), emphasizing the models' adaptability to previously unseen, out-of-domain modalities. Integrating LoRA aims to enhance forecasting performance while reducing inefficiencies associated with fine-tuning large models on limited domain-specific data. Our experiments show that LoRA fine-tuning of time series foundational models significantly improves forecasting, achieving results comparable to state-of-the-art models trained from scratch on similar modalities. We conduct comprehensive ablation studies to demonstrate the trade-offs between the number of tunable parameters and forecasting performance and assess the impact of varying LoRA matrix ranks on model performance.

Divij Gupta
Anubhav Bhatti
Suraj Parmar
Chen Dan
Yuwei Liu
Bingjie Shen
San Lee

International Conference on Multimodal Interaction


DGCformer: Deep Graph Clustering Transformer for Multivariate Time Series Forecasting

Abstract: Multivariate time series forecasting tasks are usually conducted in a channel-dependent (CD) way since it can incorporate more variable-relevant information. However, it may also involve a lot of irrelevant variables, and this even leads to worse performance than the channel-independent (CI) strategy. This paper combines the strengths of both strategies and proposes the Deep Graph Clustering Transformer (DGCformer) for multivariate time series forecasting. Specifically, it first groups these relevant variables by a graph convolutional network integrated with an autoencoder, and a former-latter masked self-attention mechanism is then considered with the CD strategy being applied to each group of variables while the CI one for different groups. Extensive experimental results on eight datasets demonstrate the superiority of our method against state-of-the-art models, and our code will be publicly available upon acceptance.

Qinshuo Liu
Yanwen Fang
Pengtao Jiang
Guodong Li


Forecasting with Hyper-Trees

Abstract: We introduce Hyper-Trees as a novel framework for modeling time series data using gradient boosted trees. Unlike conventional tree-based approaches that forecast time series directly, Hyper-Trees learn the parameters of a target time series model, such as ARIMA or Exponential Smoothing, as functions of features. These parameters are then used by the target model to generate the final forecasts. Our framework combines the effectiveness of decision trees on tabular data with classical forecasting models, thereby inducing a time series inductive bias into tree-based models. To resolve the scaling limitations of boosted trees when estimating a high-dimensional set of target model parameters, we combine decision trees and neural networks within a unified framework. In this hybrid approach, the trees generate informative representations from the input features, which a shallow network then uses as input to learn the parameters of a time series model. With our research, we explore the effectiveness of Hyper-Trees across a range of forecasting tasks and extend tree-based modeling beyond its conventional use in time series analysis.


ReCycle: Fast and Efficient Long Time Series Forecasting with Residual Cyclic Transformers

Abstract: Transformers have recently gained prominence in long time series forecasting by elevating accuracies in a variety of use cases. Regrettably, in the race for better predictive performance the overhead of model architectures has grown onerous, leading to models with computational demand infeasible for most practical applications. To bridge the gap between high method complexity and realistic computational resources, we introduce the Residual Cyclic Transformer, ReCycle. ReCycle utilizes primary cycle compression to address the computational complexity of the attention mechanism in long time series. By learning residuals from refined smoothing average techniques, ReCycle surpasses state-of-the-art accuracy in a variety of application use cases. The reliable and explainable fallback behavior ensured by simple, yet robust, smoothing average techniques additionally lowers the barrier for user acceptance. At the same time, our approach reduces the run time and energy consumption by more than an order of magnitude, making both training and inference feasible on low-performance, low-power and edge computing devices. Code is available at https://github.com/Helmholtz-AI-Energy/ReCycle

Arvid Weyrauch
Thomas Steens
Oskar Taubert
Benedikt Hanke
Aslan Eqbal
Ewa Götz
Achim Streit
Markus Götz
Charlotte Debus


CVTN: Cross Variable and Temporal Integration for Time Series Forecasting

Abstract: In multivariate time series forecasting, the Transformer architecture encounters two significant challenges: effectively mining features from historical sequences and avoiding overfitting during the learning of temporal dependencies. To tackle these challenges, this paper deconstructs time series forecasting into the learning of historical sequences and prediction sequences, introducing the Cross-Variable and Time Network (CVTN). This unique method divides multivariate time series forecasting into two phases: cross-variable learning for effectively mining fea tures from historical sequences, and cross-time learning to capture the temporal dependencies of prediction sequences. Separating these two phases helps avoid the impact of overfitting in cross-time learning on cross-variable learning. Exten sive experiments on various real-world datasets have confirmed its state-of-the-art (SOTA) performance. CVTN emphasizes three key dimensions in time series fore casting: the short-term and long-term nature of time series (locality and longevity), feature mining from both historical and prediction sequences, and the integration of cross-variable and cross-time learning. This approach not only advances the current state of time series forecasting but also provides a more comprehensive framework for future research in this field.


SST: Multi-Scale Hybrid Mamba-Transformer Experts for Time Series Forecasting

Abstract: Time series forecasting has made significant advances, including with Transformer-based models. The attention mechanism in Transformer effectively captures temporal dependencies by attending to all past inputs simultaneously. However, its quadratic complexity with respect to sequence length limits the scalability for long-range modeling. Recent state space models (SSMs) such as Mamba offer a promising alternative by achieving linear complexity without attention. Yet, Mamba compresses historical information into a fixed-size latent state, potentially causing information loss and limiting representational effectiveness. This raises a key research question: Can we design a hybrid Mamba-Transformer architecture that is both effective and efficient for time series forecasting? To address it, we adapt a hybrid Mamba-Transformer architecture Mambaformer, originally proposed for language modeling, to the time series domain. Preliminary experiments reveal that naively stacking Mamba and Transformer layers in Mambaformer is suboptimal for time series forecasting, due to an information interference problem. To mitigate this issue, we introduce a new time series decomposition strategy that separates time series into long-range patterns and short-range variations. Then we show that Mamba excels at capturing long-term structures, while Transformer is more effective at modeling short-term dynamics. Building on this insight, we propose State Space Transformer (SST), a multi-scale hybrid model with expert modules: a Mamba expert for long-range patterns and a Transformer expert for short-term variations. SST also employs a multi-scale patching mechanism to adaptively adjust time series resolution: low resolution for long-term patterns and high resolution for short-term variations. Experiments show that SST obtains SOTA performance with linear scalability. The code is at https://github.com/XiongxiaoXu/SST.

Xiongxiao Xu
Canyu Chen
Yueqing Liang
Baixiang Huang
Guangji Bai
Liang Zhao
Kai Shu


TimeGPT in Load Forecasting: A Large Time Series Model Perspective

Abstract: Machine learning models have made significant progress in load forecasting, but their forecast accuracy is limited in cases where historical load data is scarce. Inspired by the outstanding performance of large language models (LLMs) in computer vision and natural language processing, this paper aims to discuss the potential of large time series models in load forecasting with scarce historical data. Specifically, the large time series model is constructed as a time series generative pre-trained transformer (TimeGPT), which is trained on massive and diverse time series datasets consisting of 100 billion data points (e.g., finance, transportation, banking, web traffic, weather, energy, healthcare, etc.). Then, the scarce historical load data is used to fine-tune the TimeGPT, which helps it to adapt to the data distribution and characteristics associated with load forecasting. Simulation results show that TimeGPT outperforms the benchmarks (e.g., popular machine learning models and statistical models) for load forecasting on several real datasets with scarce training samples, particularly for short look-ahead times. However, it cannot be guaranteed that TimeGPT is always superior to benchmarks for load forecasting with scarce data, since the performance of TimeGPT may be affected by the distribution differences between the load data and the training data. In practical applications, we can divide the historical data into a training set and a validation set, and then use the validation set loss to decide whether TimeGPT is the best choice for a specific dataset.

Wenlong Liao
Fernando Porte-Agel
Jiannong Fang
Christian Rehtanz
Shouxiang Wang
Dechang Yang
Zhe Yang


An Analysis of Linear Time Series Forecasting Models

Abstract: Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature normalisation that improves model generalisation. In this paper we analyse the sets of functions expressible using these linear model architectures. In so doing we show that several popular variants of linear models for time series forecasting are equivalent and functionally indistinguishable from standard, unconstrained linear regression. We characterise the model classes for each linear variant. We demonstrate that each model can be reinterpreted as unconstrained linear regression over a suitably augmented feature set, and therefore admit closed-form solutions when using a mean-squared loss function. We provide experimental evidence that the models under inspection learn nearly identical solutions, and finally demonstrate that the simpler closed form solutions are superior forecasters across 72% of test settings.


Leveraging Non-Decimated Wavelet Packet Features and Transformer Models for Time Series Forecasting

Abstract: This article combines wavelet analysis techniques with machine learning methods for univariate time series forecasting, focusing on three main contributions. Firstly, we consider the use of Daubechies wavelets with different numbers of vanishing moments as input features to both non-temporal and temporal forecasting methods, by selecting these numbers during the cross-validation phase. Secondly, we compare the use of both the non-decimated wavelet transform and the non-decimated wavelet packet transform for computing these features, the latter providing a much larger set of potentially useful coefficient vectors. The wavelet coefficients are computed using a shifted version of the typical pyramidal algorithm to ensure no leakage of future information into these inputs. Thirdly, we evaluate the use of these wavelet features on a significantly wider set of forecasting methods than previous studies, including both temporal and non-temporal models, and both statistical and deep learning-based methods. The latter include state-of-the-art transformer-based neural network architectures. Our experiments suggest significant benefit in replacing higher-order lagged features with wavelet features across all examined non-temporal methods for one-step-forward forecasting, and modest benefit when used as inputs for temporal deep learning-based models for long-horizon forecasting.


Chronos: Learning the Language of Time Series

Abstract: We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.

Abdul Fatir Ansari
Lorenzo Stella
Caner Turkmen
Xiyuan Zhang
Pedro Mercado
Huibin Shen
Oleksandr Shchur
Syama Sundar Rangapuram
Sebastian Pineda Arango
Shubham Kapoor
Jasper Zschiegner
Danielle C. Maddix
Hao Wang
Michael W. Mahoney
Kari Torkkola
Andrew Gordon Wilson
Michael Bohlke-Schneider
Yuyang Wang


A Segmentation Foundation Model for Diverse-type Tumors

Abstract: Large pre-trained models with their numerous model parameters and extensive training datasets have shown excellent performance in various tasks. Many publicly available medical image datasets do not have a sufficient amount of data so there are few large-scale models in medical imaging. We propose a large-scale Tumor Segmentation Foundation Model (TSFM) with 1.6 billion parameters using Resblock-backbone and Transformer-bottleneck,which has good transfer ability for downstream tasks. To make TSFM exhibit good performance in tumor segmentation, we make full use of the strong spatial correlation between tumors and organs in the medical image, innovatively fuse 7 tumor datasets and 3 multi-organ datasets to build a 3D medical dataset pool, including 2779 cases with totally 300k medical images, whose size currently exceeds many other single publicly available datasets. TSFM is the pre-trained model for medical image segmentation, which also can be transferred to multiple downstream tasks for fine-tuning learning. The average performance of our pre-trained model is 2% higher than that of nnU-Net across various tumor types. In the transfer learning task, TSFM only needs 5% training epochs of nnU-Net to achieve similar performance and can surpass nnU-Net by 2% on average with 10% training epoch. Pre-trained TSFM and its code will be released soon.

Jianhao Xie
Ziang Zhang
Guibo Luo
Yuesheng Zhu


Considering Nonstationary within Multivariate Time Series with Variational Hierarchical Transformer for Forecasting

Abstract: The forecasting of Multivariate Time Series (MTS) has long been an important but challenging task. Due to the non-stationary problem across long-distance time steps, previous studies primarily adopt stationarization method to attenuate the non-stationary problem of the original series for better predictability. However, existing methods always adopt the stationarized series, which ignores the inherent non-stationarity, and has difficulty in modeling MTS with complex distributions due to the lack of stochasticity. To tackle these problems, we first develop a powerful hierarchical probabilistic generative module to consider the non-stationarity and stochastic characteristics within MTS, and then combine it with transformer for a well-defined variational generative dynamic model named Hierarchical Time series Variational Transformer (HTV-Trans), which recovers the intrinsic non-stationary information into temporal dependencies. Being a powerful probabilistic model, HTV-Trans is utilized to learn expressive representations of MTS and applied to forecasting tasks. Extensive experiments on diverse datasets show the efficiency of HTV-Trans on MTS forecasting tasks

AAAI Conference on Artificial Intelligence


Hyperparameter Tuning MLPs for Probabilistic Time Series Forecasting

Abstract: Time series forecasting attempts to predict future events by analyzing past trends and patterns. Although well researched, certain critical aspects pertaining to the use of deep learning in time series forecasting remain ambiguous. Our research primarily focuses on examining the impact of specific hyperparameters related to time series, such as context length and validation strategy, on the performance of the state-of-the-art MLP model in time series forecasting. We have conducted a comprehensive series of experiments involving 4800 configurations per dataset across 20 time series forecasting datasets, and our findings demonstrate the importance of tuning these parameters. Furthermore, in this work, we introduce the largest metadataset for timeseries forecasting to date, named TSBench, comprising 97200 evaluations, which is a twentyfold increase compared to previous works in the field. Finally, we demonstrate the utility of the created metadataset on multi-fidelity hyperparameter optimization tasks.

Kiran Madhusudhanan
Shayan Jawed
Lars Schmidt-Thieme

Pacific-Asia Conference on Knowledge Discovery and Data Mining


EXPRTS: Exploring and Probing the Robustness of Time Series Forecasting Models

Abstract: When deploying time series forecasting models based on machine learning to real world settings, one often encounter situations where the data distribution drifts. Such drifts expose the forecasting models to out-of-distribution (OOD) data, and machine learning models lack robustness in these settings. Robustness can be improved by using deep generative models or genetic algorithms to augment time series datasets, but these approaches lack interpretability and are computationally expensive. In this work, we develop an interpretable and simple framework for generating time series. Our method combines time-series decompositions with analytic functions, and is able to generate time series with characteristics matching both in- and out-of-distribution data. This approach allows users to generate new time series in an interpretable fashion, which can be used to augment the dataset and improve forecasting robustness. We demonstrate our framework through EXPRTS, a visual analytics tool designed for univariate time series forecasting models and datasets. Different visualizations of the data distribution, forecasting errors and single time series instances enable users to explore time series datasets, apply transformations, and evaluate forecasting model robustness across diverse scenarios. We show how our framework can generate meaningful OOD time series that improve model robustness, and we validate EXPRTS effectiveness and usability through three use-cases and a user study.

Håkon Hanisch Kjærnli
Lluis Mas-Ribas
Hans Jakob Håland
Vegard Sjåvik
Aida Ashrafi
Helge Langseth
Odd Erik Gundersen


Towards Foundation Time Series Model: To Synthesize Or Not To Synthesize?

Abstract: The industry is rich in cases when we are required to make forecasting for large amounts of time series at once. However, we might be in a situation where we can not afford to train a separate model for each of them. Such issue in time series modeling remains without due attention. The remedy for this setting is the establishment of a foundation model. Such a model is expected to work in zero-shot and few-shot regimes. However, what should we take as a training dataset for such kind of model? Witnessing the benefits from the enrichment of NLP datasets with artificially-generated data, we might want to adopt their experience for time series. In contrast to natural language, the process of generation of synthetic time series data is even more favorable because it provides full control of series patterns, time horizons, and number of samples. In this work, we consider the essential question if it is advantageous to train a foundation model on synthetic data or it is better to utilize only a limited number of real-life examples. Our experiments are conducted only for regular time series and speak in favor of leveraging solely the real time series. Moreover, the choice of the proper source dataset strongly influences the performance during inference. When provided access even to a limited quantity of short time series data, employing it within a supervised framework yields more favorable results than training on a larger volume of synthetic data. The code for our experiments is publicly available on Github \url{https://github.com/sb-ai-lab/synthesize_or_not}.

Kseniia Kuvshinova
Olga Tsymboi
Alina Kostromina
Dmitry Simakov
Elizaveta Kovtun


TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables

Abstract: Deep models have demonstrated remarkable performance in time series forecasting. However, due to the partially-observed nature of real-world applications, solely focusing on the target of interest, so-called endogenous variables, is usually insufficient to guarantee accurate forecasting. Notably, a system is often recorded into multiple variables, where the exogenous variables can provide valuable external information for endogenous variables. Thus, unlike well-established multivariate or univariate forecasting paradigms that either treat all the variables equally or ignore exogenous information, this paper focuses on a more practical setting: time series forecasting with exogenous variables. We propose a novel approach, TimeXer, to ingest external information to enhance the forecasting of endogenous variables. With deftly designed embedding layers, TimeXer empowers the canonical Transformer with the ability to reconcile endogenous and exogenous information, where patch-wise self-attention and variate-wise cross-attention are used simultaneously. Moreover, global endogenous tokens are learned to effectively bridge the causal information underlying exogenous series into endogenous temporal patches. Experimentally, TimeXer achieves consistent state-of-the-art performance on twelve real-world forecasting benchmarks and exhibits notable generality and scalability. Code is available at this repository: https://github.com/thuml/TimeXer.

Yuxuan Wang
Haixu Wu
Jiaxiang Dong
Guo Qin
Haoran Zhang
Yong Liu
Yunzhong Qiu
Jianmin Wang
Mingsheng Long


Generative Pretrained Hierarchical Transformer for Time Series Forecasting

Abstract: 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 \textbf{GPHT}. There are two aspects of key designs in GPHT. On the one hand, we advocate for constructing a mixed dataset under the channel-independent assumption 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, effectively modeling temporal dependencies in the output series. Importantly, no customized forecasting head is required, enabling \textit{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. We make our codes publicly available\footnote{https://github.com/icantnamemyself/GPHT}.

Zhiding Liu
Jiqian Yang
Mingyue Cheng
Yucong Luo
Zhi Li


Time Series Forecasting with LLMs: Understanding and Enhancing Model Capabilities

Abstract: Large language models (LLMs) have been applied in many fields and have developed rapidly in recent years. As a classic machine learning task, time series forecasting has recently been boosted by LLMs. Recent works treat large language models as \emph{zero-shot} time series reasoners without further fine-tuning, which achieves remarkable performance. However, there are some unexplored research problems when applying LLMs for time series forecasting under the zero-shot setting. For instance, the LLMs' preferences for the input time series are less understood. In this paper, by comparing LLMs with traditional time series forecasting models, we observe many interesting properties of LLMs in the context of time series forecasting. First, our study shows that LLMs perform well in predicting time series with clear patterns and trends, but face challenges with datasets lacking periodicity. This observation can be explained by the ability of LLMs to recognize the underlying period within datasets, which is supported by our experiments. In addition, the input strategy is investigated, and it is found that incorporating external knowledge and adopting natural language paraphrases substantially improve the predictive performance of LLMs for time series. Overall, our study contributes insight into LLMs' advantages and limitations in time series forecasting under different conditions.

Hua Tang
Chong Zhang
Mingyu Jin
Qinkai Yu
Zhenting Wang
Xiaobo Jin
Yongfeng Zhang
Mengnan Du


SAMformer: Unlocking the Potential of Transformers in Time Series Forecasting with Sharpness-Aware Minimization and Channel-Wise Attention

Abstract: Transformer-based architectures achieved breakthrough performance in natural language processing and computer vision, yet they remain inferior to simpler linear baselines in multivariate long-term forecasting. To better understand this phenomenon, we start by studying a toy linear forecasting problem for which we show that transformers are incapable of converging to their true solution despite their high expressive power. We further identify the attention of transformers as being responsible for this low generalization capacity. Building upon this insight, we propose a shallow lightweight transformer model that successfully escapes bad local minima when optimized with sharpness-aware optimization. We empirically demonstrate that this result extends to all commonly used real-world multivariate time series datasets. In particular, SAMformer surpasses current state-of-the-art methods and is on par with the biggest foundation model MOIRAI while having significantly fewer parameters. The code is available at https://github.com/romilbert/samformer.

Romain Ilbert
Ambroise Odonnat
Vasilii Feofanov
Aladin Virmaux
Giuseppe Paolo
Themis Palpanas
Ievgen Redko


Only the Curve Shape Matters: Training Foundation Models for Zero-Shot Multivariate Time Series Forecasting through Next Curve Shape Prediction

Abstract: We present General Time Transformer (GTT), an encoder-only style foundation model for zero-shot multivariate time series forecasting. GTT is pretrained on a large dataset of 200M high-quality time series samples spanning diverse domains. In our proposed framework, the task of multivariate time series forecasting is formulated as a channel-wise next curve shape prediction problem, where each time series sample is represented as a sequence of non-overlapping curve shapes with a unified numerical magnitude. GTT is trained to predict the next curve shape based on a window of past curve shapes in a channel-wise manner. Experimental results demonstrate that GTT exhibits superior zero-shot multivariate forecasting capabilities on unseen time series datasets, even surpassing state-of-the-art supervised baselines. Additionally, we investigate the impact of varying GTT model parameters and training dataset scales, observing that the scaling law also holds in the context of zero-shot multivariate time series forecasting.


Sparse-VQ Transformer: An FFN-Free Framework with Vector Quantization for Enhanced Time Series Forecasting

Abstract: Time series analysis is vital for numerous applications, and transformers have become increasingly prominent in this domain. Leading methods customize the transformer architecture from NLP and CV, utilizing a patching technique to convert continuous signals into segments. Yet, time series data are uniquely challenging due to significant distribution shifts and intrinsic noise levels. To address these two challenges,we introduce the Sparse Vector Quantized FFN-Free Transformer (Sparse-VQ). Our methodology capitalizes on a sparse vector quantization technique coupled with Reverse Instance Normalization (RevIN) to reduce noise impact and capture sufficient statistics for forecasting, serving as an alternative to the Feed-Forward layer (FFN) in the transformer architecture. Our FFN-free approach trims the parameter count, enhancing computational efficiency and reducing overfitting. Through evaluations across ten benchmark datasets, including the newly introduced CAISO dataset, Sparse-VQ surpasses leading models with a 7.84% and 4.17% decrease in MAE for univariate and multivariate time series forecasting, respectively. Moreover, it can be seamlessly integrated with existing transformer-based models to elevate their performance.

Yanjun Zhao
Tian Zhou
Chao Chen
Liang Sun
Yi Qian
Rong Jin

IEEE International Conference on Acoustics, Speech, and Signal Processing


Attention as Robust Representation for Time Series Forecasting

Abstract: Time series forecasting is essential for many practical applications, with the adoption of transformer-based models on the rise due to their impressive performance in NLP and CV. Transformers' key feature, the attention mechanism, dynamically fusing embeddings to enhance data representation, often relegating attention weights to a byproduct role. Yet, time series data, characterized by noise and non-stationarity, poses significant forecasting challenges. Our approach elevates attention weights as the primary representation for time series, capitalizing on the temporal relationships among data points to improve forecasting accuracy. Our study shows that an attention map, structured using global landmarks and local windows, acts as a robust kernel representation for data points, withstanding noise and shifts in distribution. Our method outperforms state-of-the-art models, reducing mean squared error (MSE) in multivariate time series forecasting by a notable 3.6% without altering the core neural network architecture. It serves as a versatile component that can readily replace recent patching based embedding schemes in transformer-based models, boosting their performance.

PeiSong Niu
Tian Zhou
Xue Wang
Liang Sun
Rong Jin


MOMENT: A Family of Open Time-series Foundation Models

Abstract: We introduce MOMENT, a family of open-source foundation models for general-purpose time series analysis. Pre-training large models on time series data is challenging due to (1) the absence of a large and cohesive public time series repository, and (2) diverse time series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time series, called the Time series Pile, and systematically tackle time series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time series models. Pre-trained models (AutonLab/MOMENT-1-large) and Time Series Pile (AutonLab/Timeseries-PILE) are available on Huggingface.

Mononito Goswami
Konrad Szafer
Arjun Choudhry
Yifu Cai
Shuo Li
Artur Dubrawski


A Survey on Transformer Compression

Abstract: Transformer plays a vital role in the realms of natural language processing (NLP) and computer vision (CV), specially for constructing large language models (LLM) and large vision models (LVM). Model compression methods reduce the memory and computational cost of Transformer, which is a necessary step to implement large language/vision models on practical devices. Given the unique architecture of Transformer, featuring alternative attention and feedforward neural network (FFN) modules, specific compression techniques are usually required. The efficiency of these compression methods is also paramount, as retraining large models on the entire training dataset is usually impractical. This survey provides a comprehensive review of recent compression methods, with a specific focus on their application to Transformer-based models. The compression methods are primarily categorized into pruning, quantization, knowledge distillation, and efficient architecture design (Mamba, RetNet, RWKV, etc.). In each category, we discuss compression methods for both language and vision tasks, highlighting common underlying principles. Finally, we delve into the relation between various compression methods, and discuss further directions in this domain.

Yehui Tang
Yunhe Wang
Jianyuan Guo
Zhijun Tu
Kai Han
Hailin Hu
Dacheng Tao


Unified Training of Universal Time Series Forecasting Transformers

Abstract: 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, data, and model weights can be found at https://github.com/SalesforceAIResearch/uni2ts.

Gerald Woo
Chenghao Liu
Akshat Kumar
Caiming Xiong
Silvio Savarese
Doyen Sahoo


Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting

Abstract: Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with adaptive pathways. It integrates both temporal resolution and temporal distance for multi-scale modeling. Multi-scale division divides the time series into different temporal resolutions using patches of various sizes. Based on the division of each scale, dual attention is performed over these patches to capture global correlations and local details as temporal dependencies. We further enrich the multi-scale Transformer with adaptive pathways, which adaptively adjust the multi-scale modeling process based on the varying temporal dynamics of the input, improving the accuracy and generalization of Pathformer. Extensive experiments on eleven real-world datasets demonstrate that Pathformer not only achieves state-of-the-art performance by surpassing all current models but also exhibits stronger generalization abilities under various transfer scenarios. The code is made available at https://github.com/decisionintelligence/pathformer.

Peng Chen
Yingying Zhang
Yunyao Cheng
Yang Shu
Yihang Wang
Qingsong Wen
Bin Yang
Chenjuan Guo

International Conference on Learning Representations


AutoTimes: Autoregressive Time Series Forecasters via Large Language Models

Abstract: 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 $5\times$ training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

Yong Liu
Guo Qin
Xiangdong Huang
Jianmin Wang
Mingsheng Long


Large Language Models for Time Series: A Survey

Abstract: Large Language Models (LLMs) have seen significant use in domains such as natural language processing and computer vision. Going beyond text, image and graphics, LLMs present a significant potential for analysis of time series data, benefiting domains such as climate, IoT, healthcare, traffic, audio and finance. This survey paper provides an in-depth exploration and a detailed taxonomy of the various methodologies employed to harness the power of LLMs for time series analysis. We address the inherent challenge of bridging the gap between LLMs' original text data training and the numerical nature of time series data, and explore strategies for transferring and distilling knowledge from LLMs to numerical time series analysis. We detail various methodologies, including (1) direct prompting of LLMs, (2) time series quantization, (3) aligning techniques, (4) utilization of the vision modality as a bridging mechanism, and (5) the combination of LLMs with tools. Additionally, this survey offers a comprehensive overview of the existing multimodal time series and text datasets and delves into the challenges and future opportunities of this emerging field. We maintain an up-to-date Github repository which includes all the papers and datasets discussed in the survey.

Xiyuan Zhang
Ranak Roy Chowdhury
Rajesh K. Gupta
Jingbo Shang

International Joint Conference on Artificial Intelligence


IN-Flow: Instance Normalization Flow for Non-stationary Time Series Forecasting

Abstract: Due to the non-stationarity of time series, the distribution shift problem largely hinders the performance of time series forecasting. Existing solutions either rely on using certain statistics to specify the shift, or developing specific mechanisms for certain network architectures. However, the former would fail for the unknown shift beyond simple statistics, while the latter has limited compatibility on different forecasting models. To overcome these problems, we first propose a decoupled formulation for time series forecasting, with no reliance on fixed statistics and no restriction on forecasting architectures. This formulation regards the removing-shift procedure as a special transformation between a raw distribution and a desired target distribution and separates it from the forecasting. Such a formulation is further formalized into a bi-level optimization problem, to enable the joint learning of the transformation (outer loop) and forecasting (inner loop). Moreover, the special requirements of expressiveness and bi-direction for the transformation motivate us to propose instance normalization flow (IN-Flow), a novel invertible network for time series transformation. Different from the classic "normalizing flow" models, IN-Flow does not aim for normalizing input to the prior distribution (e.g., Gaussian distribution) for generation, but creatively transforms time series distribution by stacking normalization layers and flow-based invertible networks, which is thus named "normalization" flow. Finally, we have conducted extensive experiments on both synthetic data and real-world data, which demonstrate the superiority of our method.

Wei Fan
Shun Zheng
Pengyang Wang
Rui Xie
Kun Yi
Qi Zhang
Jiang Bian
Yanjie Fu


A Survey of Deep Learning and Foundation Models for Time Series Forecasting

Abstract: Deep Learning has been successfully applied to many application domains, yet its advantages have been slow to emerge for time series forecasting. For example, in the well-known Makridakis (M) Competitions, hybrids of traditional statistical or machine learning techniques have only recently become the top performers. With the recent architectural advances in deep learning being applied to time series forecasting (e.g., encoder-decoders with attention, transformers, and graph neural networks), deep learning has begun to show significant advantages. Still, in the area of pandemic prediction, there remain challenges for deep learning models: the time series is not long enough for effective training, unawareness of accumulated scientific knowledge, and interpretability of the model. To this end, the development of foundation models (large deep learning models with extensive pre-training) allows models to understand patterns and acquire knowledge that can be applied to new related problems before extensive training data becomes available. Furthermore, there is a vast amount of knowledge available that deep learning models can tap into, including Knowledge Graphs and Large Language Models fine-tuned with scientific domain knowledge. There is ongoing research examining how to utilize or inject such knowledge into deep learning models. In this survey, several state-of-the-art modeling techniques are reviewed, and suggestions for further work are provided.

John A. Miller
Mohammed Aldosari
Farah Saeed
Nasid Habib Barna
Subas Rana
I. Budak Arpinar
Ninghao Liu


Transformers with Attentive Federated Aggregation for Time Series Stock Forecasting

Abstract: 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.

Chu Myaet Thwal
Ye Lin Tun
Kitae Kim
Seong-Bae Park
Choong Seon Hong

International Conference on Information Networking


MSHyper: Multi-Scale Hypergraph Transformer for Long-Range Time Series Forecasting

Abstract: Demystifying interactions between temporal patterns of different scales is fundamental to precise long-range time series forecasting. However, previous works lack the ability to model high-order interactions. To promote more comprehensive pattern interaction modeling for long-range time series forecasting, we propose a Multi-Scale Hypergraph Transformer (MSHyper) framework. Specifically, a multi-scale hypergraph is introduced to provide foundations for modeling high-order pattern interactions. Then by treating hyperedges as nodes, we also build a hyperedge graph to enhance hypergraph modeling. In addition, a tri-stage message passing mechanism is introduced to aggregate pattern information and learn the interaction strength between temporal patterns of different scales. Extensive experiments on five real-world datasets demonstrate that MSHyper achieves state-of-the-art (SOTA) performance across various settings.

Zongjiang Shang
Ling Chen
Binqing Wu
Dongliang Cui


Domain Adaptation for Time series Transformers using One-step fine-tuning

Abstract: The recent breakthrough of Transformers in deep learning has drawn significant attention of the time series community due to their ability to capture long-range dependencies. However, like other deep learning models, Transformers face limitations in time series prediction, including insufficient temporal understanding, generalization challenges, and data shift issues for the domains with limited data. Additionally, addressing the issue of catastrophic forgetting, where models forget previously learned information when exposed to new data, is another critical aspect that requires attention in enhancing the robustness of Transformers for time series tasks. To address these limitations, in this paper, we pre-train the time series Transformer model on a source domain with sufficient data and fine-tune it on the target domain with limited data. We introduce the \emph{One-step fine-tuning} approach, adding some percentage of source domain data to the target domains, providing the model with diverse time series instances. We then fine-tune the pre-trained model using a gradual unfreezing technique. This helps enhance the model's performance in time series prediction for domains with limited data. Extensive experimental results on two real-world datasets show that our approach improves over the state-of-the-art baselines by 4.35% and 11.54% for indoor temperature and wind power prediction, respectively.

Subina Khanal
Seshu Tirupathi
Giulio Zizzo
Ambrish Rawat
Torben Bach Pedersen


HiMTM: Hierarchical Multi-Scale Masked Time Series Modeling with Self-Distillation for Long-Term Forecasting

Abstract: Time series forecasting is a critical and challenging task in practical application. Recent advancements in pre-trained foundation models for time series forecasting have gained significant interest. However, current methods often overlook the multi-scale nature of time series, which is essential for accurate forecasting. To address this, we propose HiMTM, a hierarchical multi-scale masked time series modeling with self-distillation for long-term forecasting. HiMTM integrates four key components: (1) hierarchical multi-scale transformer (HMT) to capture temporal information at different scales; (2) decoupled encoder-decoder (DED) that directs the encoder towards feature extraction while the decoder focuses on pretext tasks; (3) hierarchical self-distillation (HSD) for multi-stage feature-level supervision signals during pre-training; and (4) cross-scale attention fine-tuning (CSA-FT) to capture dependencies between different scales for downstream tasks. These components collectively enhance multi-scale feature extraction in masked time series modeling, improving forecasting accuracy. Extensive experiments on seven mainstream datasets show that HiMTM surpasses state-of-the-art self-supervised and end-to-end learning methods by a considerable margin of 3.16-68.54\%. Additionally, HiMTM outperforms the latest robust self-supervised learning method, PatchTST, in cross-domain forecasting by a significant margin of 2.3\%. The effectiveness of HiMTM is further demonstrated through its application in natural gas demand forecasting.

Shubao Zhao
Ming Jin
Zhaoxiang Hou
Chengyi Yang
Zengxiang Li
Qingsong Wen
Yi Wang


The Rise of Diffusion Models in Time-Series Forecasting

Abstract: This survey delves into the application of diffusion models in time-series forecasting. Diffusion models are demonstrating state-of-the-art results in various fields of generative AI. The paper includes comprehensive background information on diffusion models, detailing their conditioning methods and reviewing their use in time-series forecasting. The analysis covers 11 specific time-series implementations, the intuition and theory behind them, the effectiveness on different datasets, and a comparison among each other. Key contributions of this work are the thorough exploration of diffusion models' applications in time-series forecasting and a chronologically ordered overview of these models. Additionally, the paper offers an insightful discussion on the current state-of-the-art in this domain and outlines potential future research directions. This serves as a valuable resource for researchers in AI and time-series analysis, offering a clear view of the latest advancements and future potential of diffusion models.


Explainable Adaptive Tree-based Model Selection for Time Series Forecasting

Abstract: Tree-based models have been successfully applied to a wide variety of tasks, including time series forecasting. They are increasingly in demand and widely accepted because of their comparatively high level of interpretability. However, many of them suffer from the overfitting problem, which limits their application in real-world decision-making. This problem becomes even more severe in online-forecasting settings where time series observations are incrementally acquired, and the distributions from which they are drawn may keep changing over time. In this context, we propose a novel method for the online selection of tree-based models using the TreeSHAP explainability method in the task of time series forecasting. We start with an arbitrary set of different tree-based models. Then, we outline a performance-based ranking with a coherent design to make TreeSHAP able to specialize the tree-based forecasters across different regions in the input time series. In this framework, adequate model selection is performed online, adaptively following drift detection in the time series. In addition, explainability is supported on three levels, namely online input importance, model selection, and model output explanation. An extensive empirical study on various real-world datasets demonstrates that our method achieves excellent or on-par results in comparison to the state-of-the-art approaches as well as several baselines.


auto-sktime: Automated Time Series Forecasting

Abstract: In today's data-driven landscape, time series forecasting is pivotal in decision-making across various sectors. Yet, the proliferation of more diverse time series data, coupled with the expanding landscape of available forecasting methods, poses significant challenges for forecasters. To meet the growing demand for efficient forecasting, we introduce auto-sktime, a novel framework for automated time series forecasting. The proposed framework uses the power of automated machine learning (AutoML) techniques to automate the creation of the entire forecasting pipeline. The framework employs Bayesian optimization, to automatically construct pipelines from statistical, machine learning (ML) and deep neural network (DNN) models. Furthermore, we propose three essential improvements to adapt AutoML to time series data. First, pipeline templates to account for the different supported forecasting models. Second, a novel warm-starting technique to start the optimization from prior optimization runs. Third, we adapt multi-fidelity optimizations to make them applicable to a search space containing statistical, ML and DNN models. Experimental results on 64 diverse real-world time series datasets demonstrate the effectiveness and efficiency of the framework, outperforming traditional methods while requiring minimal human involvement.

Marc-André Zöller
Marius Lindauer
Marco F. Huber


Sparse Transformer with Local and Seasonal Adaptation for Multivariate Time Series Forecasting

Abstract: Transformers have achieved remarkable performance in multivariate time series(MTS) forecasting due to their capability to capture long-term dependencies. However, the canonical attention mechanism has two key limitations: (1) its quadratic time complexity limits the sequence length, and (2) it generates future values from the entire historical sequence. To address this, we propose a Dozer Attention mechanism consisting of three sparse components: (1) Local, each query exclusively attends to keys within a localized window of neighboring time steps. (2) Stride, enables each query to attend to keys at predefined intervals. (3) Vary, allows queries to selectively attend to keys from a subset of the historical sequence. Notably, the size of this subset dynamically expands as forecasting horizons extend. Those three components are designed to capture essential attributes of MTS data, including locality, seasonality, and global temporal dependencies. Additionally, we present the Dozerformer Framework, incorporating the Dozer Attention mechanism for the MTS forecasting task. We evaluated the proposed Dozerformer framework with recent state-of-the-art methods on nine benchmark datasets and confirmed its superior performance. The experimental results indicate that excluding a subset of historical time steps from the time series forecasting process does not compromise accuracy while significantly improving efficiency. Code is available at https://github.com/GRYGY1215/Dozerformer.

Yifan Zhang
Rui Wu
Sergiu M. Dascalu
Frederick C. Harris


MultiResFormer: Transformer with Adaptive Multi-Resolution Modeling for General Time Series Forecasting

Abstract: Transformer-based models have greatly pushed the boundaries of time series forecasting recently. Existing methods typically encode time series data into $\textit{patches}$ using one or a fixed set of patch lengths. This, however, could result in a lack of ability to capture the variety of intricate temporal dependencies present in real-world multi-periodic time series. In this paper, we propose MultiResFormer, which dynamically models temporal variations by adaptively choosing optimal patch lengths. Concretely, at the beginning of each layer, time series data is encoded into several parallel branches, each using a detected periodicity, before going through the transformer encoder block. We conduct extensive evaluations on long- and short-term forecasting datasets comparing MultiResFormer with state-of-the-art baselines. MultiResFormer outperforms patch-based Transformer baselines on long-term forecasting tasks and also consistently outperforms CNN baselines by a large margin, while using much fewer parameters than these baselines.

Linfeng Du
Ji Xin
Alex Labach
Saba Zuberi
Maksims Volkovs
Rahul G. Krishnan


TimelyGPT: Extrapolatable Transformer Pre-training for Long-term Time-Series Forecasting in Healthcare

Abstract: Large-scale pre-trained models (PTMs) such as BERT and GPT have recently achieved great success in Natural Language Processing and Computer Vision domains. However, the development of PTMs on healthcare time-series data is lagging behind.This underscores the limitations of the existing transformer-based architectures, particularly their scalability to handle large-scale time series and ability to capture long-term temporal dependencies. In this study, we present Timely Generative Pre-trained Transformer (TimelyGPT). TimelyGPT employs an extrapolatable position (xPos) embedding to encode trend and periodic patterns into time-series representations. It also integrates recurrent attention and temporal convolution modules to effectively capture global-local temporal dependencies. We evaluated TimelyGPT on two large-scale healthcare time series datasets corresponding to continuous biosignals and irregularly-sampled time series, respectively. Our experiments show that during pre-training, TimelyGPT excels in learning time-series representations from continuously monitored biosignals and irregularly-sampled time series data commonly observed in longitudinal electronic health records (EHRs). In forecasting continuous biosignals, TimelyGPT achieves accurate extrapolation up to 6,000 timesteps of body temperature during the sleep stage transition, given a short look-up window (i.e., prompt) containing only 2,000 timesteps. For irregularly-sampled time series, TimelyGPT with a proposed time-specific inference demonstrates high top recall scores in predicting future diagnoses using early diagnostic records, effectively handling irregular intervals between clinical records. Together, we envision TimelyGPT to be useful in a broad spectrum of health domains, including long-term patient health state forecasting and patient risk trajectory prediction.

Ziyang Song
Qincheng Lu
Hao Xu
He Zhu
David L. Buckeridge
Yue Li


A projected nonlinear state-space model for forecasting time series signals

Abstract: Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy samples and predict future trajectories with uncertainty estimates while maintaining computational efficiency. Here, we propose a fast algorithm to learn and forecast nonlinear dynamics from noisy time series data. A key feature of the proposed model is kernel functions applied to projected lines, enabling fast and efficient capture of nonlinearities in the latent dynamics. Through empirical case studies and benchmarking, the model demonstrates its effectiveness in learning and forecasting complex nonlinear dynamics, offering a valuable tool for researchers and practitioners in time series analysis.

Christian Donner
Anuj Mishra
Hideaki Shimazaki