Time Series Foundation Models for Multivariate Financial Time Series Forecasting

Abstract: Financial time series forecasting presents significant challenges due to complex nonlinear relationships, temporal dependencies, variable interdependencies and limited data availability, particularly for tasks involving low-frequency data, newly listed instruments, or emerging market assets. Time Series Foundation Models (TSFMs) offer a promising solution through pretraining on diverse time series corpora followed by task-specific adaptation. This study evaluates two TSFMs (Tiny Time Mixers (TTM) and Chronos) across three financial forecasting tasks: US 10-year Treasury yield changes, EUR/USD volatility, and equity spread prediction. Results demonstrate that TTM exhibits strong transferability. When fine-tuning both the pretrained version of TTM and an untrained model with the same architecture, the pretrained version achieved 25-50% better performance when fine-tuned on limited data and 15-30% improvements even when fine-tuned on lengthier datasets. Notably, TTM's zero-shot performance outperformed naive benchmarks in volatility forecasting and equity spread prediction, with the latter demonstrating that TSFMs can surpass traditional benchmark models without fine-tuning. The pretrained model consistently required 3-10 fewer years of data to achieve comparable performance levels compared to the untrained model, demonstrating significant sample-efficiency gains. However, while TTM outperformed naive baselines, traditional specialised models matched or exceeded its performance in two of three tasks, suggesting TSFMs prioritise breadth over task-specific optimisation. These findings indicate that TSFMs, though still nascent, offer substantial promise for financial forecasting-particularly in noisy, data-constrained tasks-but achieving competitive performance likely requires domain-specific pretraining and architectural refinements tailored to financial time series characteristics.


Foundation models for time series forecasting: Application in conformal prediction

Abstract: The zero-shot capabilities of foundation models (FMs) for time series forecasting offer promising potentials in conformal prediction, as most of the available data can be allocated to calibration. This study compares the performance of Time Series Foundation Models (TSFMs) with traditional methods, including statistical models and gradient boosting, within a conformal prediction setting. Our findings highlight two key advantages of TSFMs. First, when the volume of data is limited, TSFMs provide more reliable conformalized prediction intervals than classic models, thanks to their superior predictive accuracy. Second, the calibration process is more stable because more data are used for calibration. Morever, the fewer data available, the more pronounced these benefits become, as classic models require a substantial amount of data for effective training. These results underscore the potential of foundation models in improving conformal prediction reliability in time series applications, particularly in data-constrained cases. All the code to reproduce the experiments is available.

Sami Achour
Yassine Bouher
Duong Nguyen
Nicolas Chesneau


Accurate Parameter-Efficient Test-Time Adaptation for Time Series Forecasting

Abstract: Real-world time series often exhibit a non-stationary nature, degrading the performance of pre-trained forecasting models. Test-Time Adaptation (TTA) addresses this by adjusting models during inference, but existing methods typically update the full model, increasing memory and compute costs. We propose PETSA, a parameter-efficient method that adapts forecasters at test time by only updating small calibration modules on the input and output. PETSA uses low-rank adapters and dynamic gating to adjust representations without retraining. To maintain accuracy despite limited adaptation capacity, we introduce a specialized loss combining three components: (1) a robust term, (2) a frequency-domain term to preserve periodicity, and (3) a patch-wise structural term for structural alignment. PETSA improves the adaptability of various forecasting backbones while requiring fewer parameters than baselines. Experimental results on benchmark datasets show that PETSA achieves competitive or better performance across all horizons. Our code is available at: https://github.com/BorealisAI/PETSA

Heitor R. Medeiros
Hossein Sharifi-Noghabi
Gabriel L. Oliveira
Saghar Irandoust


The language of time: a language model perspective on time-series foundation models

Abstract: With the rise of large language models, the paradigm of training foundation models with massive parameter counts on vast datasets has been adopted in multiple domains to achieve remarkable success. Time series foundation models represent a significant extension of this paradigm, demonstrating exceptional expressive power, generalization, and cross-domain transferability. However, this gives rise to a fundamental paradox: time series data reflect distinct dynamical systems, making cross-domain transfer intuitively implausible, yet this is contradicted by the models' empirical success. To resolve this paradox, this paper investigates, from both theoretical and experimental perspectives, the representation learning mechanisms and generalization capabilities of patch-based time series foundation models. We argue that such models are not merely applying a new architecture but are fundamentally generalizing the representation paradigm of language models by extending deterministic vector-based representations to latent probabilistic distributional forms. Our theoretical analysis supports this framework by demonstrating that continuous time-series patches can be faithfully quantized into a discrete vocabulary whose key statistical properties are highly consistent with those of natural language. This generalization allows time series models to inherit the robust representation and transfer abilities of large language models, thereby explaining their superior performance in temporal tasks. Ultimately, our work provides a rigorous theoretical cornerstone for understanding, evaluating, and improving the safety and reliability of large-scale time series foundation models.

Yi Xie
Yun Xiong
Zejian Shi
Hao Niu
Zhengfu Liu


UniCA: Unified Covariate Adaptation for Time Series Foundation Model

Abstract: Time Series Foundation Models (TSFMs) have achieved remarkable success through large-scale pretraining. However, their design primarily targets real-valued series, limiting their ability to handle general forecasting tasks involving diverse and often heterogeneous covariates -- such as categorical variables and multimodal data (e.g., images, text) -- which are typically task-specific and difficult to leverage during pretraining. To address this gap, we propose Unified Covariate Adaptation (UniCA), a framework to bridge TSFMs with general covariate-aware forecasting. UniCA first performs covariate homogenization to transform heterogeneous covariates into high-level homogeneous series representations and then fuses them via a unified attention-based fusion mechanism. UniCA is compatible and universal for adaptation with both homogeneous and heterogeneous covariates, incorporating extra covariate information while preserving the generalization ability of TSFMs.Extensive experiments on multiple unimodal and multimodal covariate-aware forecasting benchmarks demonstrate the superiority of UniCA, highlighting the promise of covariate-aware TSFM adaptation in real-world forecasting scenarios.Code: https://github.com/hanlu-nju/UniCA.

Lu Han
Yu Liu
Lan Li
Qiwen Deng
Jian Jiang
Yinbo Sun
Zhe Yu
Binfeng Wang
Xingyu Lu
Lintao Ma
Han-Jia Ye
De-Chuan Zhan


Scaling Transformers for Time Series Forecasting: Do Pretrained Large Models Outperform Small-Scale Alternatives?

Abstract: Large pre-trained models have demonstrated remarkable capabilities across domains, but their effectiveness in time series forecasting remains understudied. This work empirically examines whether pre-trained large-scale time series models (LSTSMs) trained on diverse datasets can outperform traditional non-pretrained small-scale transformers in forecasting tasks. We analyze state-of-the-art (SOTA) pre-trained universal time series models (e.g., Moirai, TimeGPT) alongside conventional transformers, evaluating accuracy, computational efficiency, and interpretability across multiple benchmarks. Our findings reveal the strengths and limitations of pre-trained LSTSMs, providing insights into their suitability for time series tasks compared to task-specific small-scale architectures. The results highlight scenarios where pretraining offers advantages and where simpler models remain competitive.

Sanjay Chakraborty
Ibrahim Delibasoglu
Fredrik Heintz


A Review of the Long Horizon Forecasting Problem in Time Series Analysis

Abstract: The long horizon forecasting (LHF) problem has come up in the time series literature for over the last 35 years or so. This review covers aspects of LHF in this period and how deep learning has incorporated variants of trend, seasonality, fourier and wavelet transforms, misspecification bias reduction and bandpass filters while contributing using convolutions, residual connections, sparsity reduction, strided convolutions, attention masks, SSMs, normalization methods, low-rank approximations and gating mechanisms. We highlight time series decomposition techniques, input data preprocessing and dataset windowing schemes that improve performance. Multi-layer perceptron models, recurrent neural network hybrids, self-attention models that improve and/or address the performances of the LHF problem are described, with an emphasis on the feature space construction. Ablation studies are conducted over the ETTm2 dataset in the multivariate and univariate high useful load (HUFL) forecasting contexts, evaluated over the last 4 months of the dataset. The heatmaps of MSE averages per time step over test set series in the horizon show that there is a steady increase in the error proportionate to its length except with xLSTM and Triformer models and motivate LHF as an error propagation problem. The trained models are available here: https://bit.ly/LHFModelZoo


DeepSeq: High-Throughput Single-Cell RNA Sequencing Data Labeling via Web Search-Augmented Agentic Generative AI Foundation Models

Abstract: Generative AI foundation models offer transformative potential for processing structured biological data, particularly in single-cell RNA sequencing, where datasets are rapidly scaling toward billions of cells. We propose the use of agentic foundation models with real-time web search to automate the labeling of experimental data, achieving up to 82.5% accuracy. This addresses a key bottleneck in supervised learning for structured omics data by increasing annotation throughput without manual curation and human error. Our approach enables the development of virtual cell foundation models capable of downstream tasks such as cell-typing and perturbation prediction. As data volume grows, these models may surpass human performance in labeling, paving the way for reliable inference in large-scale perturbation screens. This application demonstrates domain-specific innovation in health monitoring and diagnostics, aligned with efforts like the Human Cell Atlas and Human Tumor Atlas Network.

Saleem A. Al Dajani
Abel Sanchez
John R. Williams


ST-MTM: Masked Time Series Modeling with Seasonal-Trend Decomposition for Time Series Forecasting

Abstract: Forecasting complex time series is an important yet challenging problem that involves various industrial applications. Recently, masked time-series modeling has been proposed to effectively model temporal dependencies for forecasting by reconstructing masked segments from unmasked ones. However, since the semantic information in time series is involved in intricate temporal variations generated by multiple time series components, simply masking a raw time series ignores the inherent semantic structure, which may cause MTM to learn spurious temporal patterns present in the raw data. To capture distinct temporal semantics, we show that masked modeling techniques should address entangled patterns through a decomposition approach. Specifically, we propose ST-MTM, a masked time-series modeling framework with seasonal-trend decomposition, which includes a novel masking method for the seasonal-trend components that incorporates different temporal variations from each component. ST-MTM uses a period masking strategy for seasonal components to produce multiple masked seasonal series based on inherent multi-periodicity and a sub-series masking strategy for trend components to mask temporal regions that share similar variations. The proposed masking method presents an effective pre-training task for learning intricate temporal variations and dependencies. Additionally, ST-MTM introduces a contrastive learning task to support masked modeling by enhancing contextual consistency among multiple masked seasonal representations. Experimental results show that our proposed ST-MTM achieves consistently superior forecasting performance compared to existing masked modeling, contrastive learning, and supervised forecasting methods.


Tailored Architectures for Time Series Forecasting: Evaluating Deep Learning Models on Gaussian Process-Generated Data

Abstract: Developments in Deep Learning have significantly improved time series forecasting by enabling more accurate modeling of complex temporal dependencies inherent in sequential data. The effectiveness of such models is often demonstrated on limited sets of specific real-world data. Although this allows for comparative analysis, it still does not demonstrate how specific data characteristics align with the architectural strengths of individual models. Our research aims at uncovering clear connections between time series characteristics and particular models. We introduce a novel dataset generated using Gaussian Processes, specifically designed to display distinct, known characteristics for targeted evaluations of model adaptability to them. Furthermore, we present TimeFlex, a new model that incorporates a modular architecture tailored to handle diverse temporal dynamics, including trends and periodic patterns. This model is compared to current state-of-the-art models, offering a deeper understanding of how models perform under varied time series conditions.

IEEE International Joint Conference on Neural Network


MIRA: Medical Time Series Foundation Model for Real-World Health Data

Abstract: A unified foundation model for medical time series -- pretrained on open access and ethics board-approved medical corpora -- offers the potential to reduce annotation burdens, minimize model customization, and enable robust transfer across clinical institutions, modalities, and tasks, particularly in data-scarce or privacy-constrained environments. However, existing generalist time series foundation models struggle to handle medical time series data due to their inherent challenges, including irregular intervals, heterogeneous sampling rates, and frequent missing values. To address these challenges, we introduce MIRA, a unified foundation model specifically designed for medical time series forecasting. MIRA incorporates a Continuous-Time Rotary Positional Encoding that enables fine-grained modeling of variable time intervals, a frequency-specific mixture-of-experts layer that routes computation across latent frequency regimes to further promote temporal specialization, and a Continuous Dynamics Extrapolation Block based on Neural ODE that models the continuous trajectory of latent states, enabling accurate forecasting at arbitrary target timestamps. Pretrained on a large-scale and diverse medical corpus comprising over 454 billion time points collect from publicly available datasets, MIRA achieves reductions in forecasting errors by an average of 10% and 7% in out-of-distribution and in-distribution scenarios, respectively, when compared to other zero-shot and fine-tuned baselines. We also introduce a comprehensive benchmark spanning multiple downstream clinical tasks, establishing a foundation for future research in medical time series modeling.

Hao Li
Bowen Deng
Chang Xu
Zhiyuan Feng
Viktor Schlegel
Yu-Hao Huang
Yizheng Sun
Jingyuan Sun
Kailai Yang
Yiyao Yu
Jiang Bian


Benchmarking Pre-Trained Time Series Models for Electricity Price Forecasting

Abstract: Accurate electricity price forecasting (EPF) is crucial for effective decision-making in power trading on the spot market. While recent advances in generative artificial intelligence (GenAI) and pre-trained large language models (LLMs) have inspired the development of numerous time series foundation models (TSFMs) for time series forecasting, their effectiveness in EPF remains uncertain. To address this gap, we benchmark several state-of-the-art pretrained models--Chronos-Bolt, Chronos-T5, TimesFM, Moirai, Time-MoE, and TimeGPT--against established statistical and machine learning (ML) methods for EPF. Using 2024 day-ahead auction (DAA) electricity prices from Germany, France, the Netherlands, Austria, and Belgium, we generate daily forecasts with a one-day horizon. Chronos-Bolt and Time-MoE emerge as the strongest among the TSFMs, performing on par with traditional models. However, the biseasonal MSTL model, which captures daily and weekly seasonality, stands out for its consistent performance across countries and evaluation metrics, with no TSFM statistically outperforming it.

Timothée Hornek Amir Sartipi
Igor Tchappi
Gilbert Fridgen


LightGTS: A Lightweight General Time Series Forecasting Model

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

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

International Conference on Machine Learning


FaCTR: Factorized Channel-Temporal Representation Transformers for Efficient Time Series Forecasting

Abstract: While Transformers excel in language and vision-where inputs are semantically rich and exhibit univariate dependency structures-their architectural complexity leads to diminishing returns in time series forecasting. Time series data is characterized by low per-timestep information density and complex dependencies across channels and covariates, requiring conditioning on structured variable interactions. To address this mismatch and overparameterization, we propose FaCTR, a lightweight spatiotemporal Transformer with an explicitly structural design. FaCTR injects dynamic, symmetric cross-channel interactions-modeled via a low-rank Factorization Machine into temporally contextualized patch embeddings through a learnable gating mechanism. It further encodes static and dynamic covariates for multivariate conditioning. Despite its compact design, FaCTR achieves state-of-the-art performance on eleven public forecasting benchmarks spanning both short-term and long-term horizons, with its largest variant using close to only 400K parameters-on average 50x smaller than competitive spatiotemporal transformer baselines. In addition, its structured design enables interpretability through cross-channel influence scores-an essential requirement for real-world decision-making. Finally, FaCTR supports self-supervised pretraining, positioning it as a compact yet versatile foundation for downstream time series tasks.


RATFM: Retrieval-augmented Time Series Foundation Model for Anomaly Detection

Abstract: Inspired by the success of large language models (LLMs) in natural language processing, recent research has explored the building of time series foundation models and applied them to tasks such as forecasting, classification, and anomaly detection. However, their performances vary between different domains and tasks. In LLM-based approaches, test-time adaptation using example-based prompting has become common, owing to the high cost of retraining. In the context of anomaly detection, which is the focus of this study, providing normal examples from the target domain can also be effective. However, time series foundation models do not naturally acquire the ability to interpret or utilize examples or instructions, because the nature of time series data used during training does not encourage such capabilities. To address this limitation, we propose a retrieval augmented time series foundation model (RATFM), which enables pretrained time series foundation models to incorporate examples of test-time adaptation. We show that RATFM achieves a performance comparable to that of in-domain fine-tuning while avoiding domain-dependent fine-tuning. Experiments on the UCR Anomaly Archive, a multi-domain dataset including nine domains, confirms the effectiveness of the proposed approach.


Probabilistic Forecasting for Building Energy Systems using Time-Series Foundation Models

Abstract: Decision-making in building energy systems critically depends on the predictive accuracy of relevant time-series models. In scenarios lacking extensive data from a target building, foundation models (FMs) represent a promising technology that can leverage prior knowledge from vast and diverse pre-training datasets to construct accurate probabilistic predictors for use in decision-making tools. This paper investigates the applicability and fine-tuning strategies of time-series foundation models (TSFMs) in building energy forecasting. We analyze both full fine-tuning and parameter-efficient fine-tuning approaches, particularly low-rank adaptation (LoRA), by using real-world data from a commercial net-zero energy building to capture signals such as room occupancy, carbon emissions, plug loads, and HVAC energy consumption. Our analysis reveals that the zero-shot predictive performance of TSFMs is generally suboptimal. To address this shortcoming, we demonstrate that employing either full fine-tuning or parameter-efficient fine-tuning significantly enhances forecasting accuracy, even with limited historical data. Notably, fine-tuning with low-rank adaptation (LoRA) substantially reduces computational costs without sacrificing accuracy. Furthermore, fine-tuned TSFMs consistently outperform state-of-the-art deep forecasting models (e.g., temporal fusion transformers) in accuracy, robustness, and generalization across varying building zones and seasonal conditions. These results underline the efficacy of TSFMs for practical, data-constrained building energy management systems, enabling improved decision-making in pursuit of energy efficiency and sustainability.

Young Jin Park
Francois Germain
Jing Liu
Ye Wang
Toshiaki Koike-Akino
Gordon Wichern
Navid Azizan
Christopher R. Laughman
Ankush Chakrabarty


Generalisation Bounds of Zero-Shot Economic Forecasting using Time Series Foundation Models

Abstract: This study investigates zero-shot forecasting capabilities of Time Series Foundation Models (TSFMs) for macroeconomic indicators. We apply TSFMs to forecasting economic indicators under univariate conditions, bypassing the need for train bespoke econometric models using and extensive training datasets. Our experiments were conducted on a case study dataset, without additional customisation. We rigorously back-tested three state-of-the-art TSFMs (Chronos, TimeGPT and Moirai) under data-scarce conditions and structural breaks. Our results demonstrate that appropriately engineered TSFMs can internalise rich economic dynamics, accommodate regime shifts, and deliver well-behaved uncertainty estimates out of the box, while matching state-of-the-art multivariate models on this domain. Our findings suggest that, without any fine-tuning, TSFMs can match or exceed classical models during stable economic conditions. However, they are vulnerable to degradation in performances during periods of rapid shocks. The findings offer guidance to practitioners on when zero-shot deployments are viable for macroeconomic monitoring and strategic planning.

Jittarin Jetwiriyanon
Teo Susnjak
Surangika Ranathunga

Machine Learning and Knowledge Extraction


Synthetic Time Series Forecasting with Transformer Architectures: Extensive Simulation Benchmarks

Abstract: Time series forecasting plays a critical role in domains such as energy, finance, and healthcare, where accurate predictions inform decision-making under uncertainty. Although Transformer-based models have demonstrated success in sequential modeling, their adoption for time series remains limited by challenges such as noise sensitivity, long-range dependencies, and a lack of inductive bias for temporal structure. In this work, we present a unified and principled framework for benchmarking three prominent Transformer forecasting architectures-Autoformer, Informer, and Patchtst-each evaluated through three architectural variants: Minimal, Standard, and Full, representing increasing levels of complexity and modeling capacity. We conduct over 1500 controlled experiments on a suite of ten synthetic signals, spanning five patch lengths and five forecast horizons under both clean and noisy conditions. Our analysis reveals consistent patterns across model families. To advance this landscape further, we introduce the Koopman-enhanced Transformer framework, Deep Koopformer, which integrates operator-theoretic latent state modeling to improve stability and interpretability. We demonstrate its efficacy on nonlinear and chaotic dynamical systems. Our results highlight Koopman based Transformer as a promising hybrid approach for robust, interpretable, and theoretically grounded time series forecasting in noisy and complex real-world conditions.


Time-o1: Time-Series Forecasting Needs Transformed Label Alignment

Abstract: Training time-series forecast models presents unique challenges in designing effective learning objectives. Existing methods predominantly utilize the temporal mean squared error, which faces two critical challenges: (1) label autocorrelation, which leads to bias from the label sequence likelihood; (2) excessive amount of tasks, which increases with the forecast horizon and complicates optimization. To address these challenges, we propose Time-o1, a transformation-augmented learning objective tailored for time-series forecasting. The central idea is to transform the label sequence into decorrelated components with discriminated significance. Models are then trained to align the most significant components, thereby effectively mitigating label autocorrelation and reducing task amount. Extensive experiments demonstrate that Time-o1 achieves state-of-the-art performance and is compatible with various forecast models. Code is available at https://github.com/Master-PLC/Time-o1.

Hao Wang
Licheng Pan
Zhichao Chen
Xu Chen
Qingyang Dai
Lei Wang
Haoxuan Li
Zhouchen Lin


Time to Embed: Unlocking Foundation Models for Time Series with Channel Descriptions

Abstract: Traditional time series models are task-specific and often depend on dataset-specific training and extensive feature engineering. While Transformer-based architectures have improved scalability, foundation models, commonplace in text, vision, and audio, remain under-explored for time series and are largely restricted to forecasting. We introduce $\textbf{CHARM}$, a foundation embedding model for multivariate time series that learns shared, transferable, and domain-aware representations. To address the unique difficulties of time series foundation learning, $\textbf{CHARM}$ incorporates architectural innovations that integrate channel-level textual descriptions while remaining invariant to channel order. The model is trained using a Joint Embedding Predictive Architecture (JEPA), with novel augmentation schemes and a loss function designed to improve interpretability and training stability. Our $7$M-parameter model achieves state-of-the-art performance across diverse downstream tasks, setting a new benchmark for time series representation learning.

Utsav Dutta
Sina Khoshfetrat Pakazad
Henrik Ohlsson


This Time is Different: An Observability Perspective on Time Series Foundation Models

Abstract: We introduce Toto, a time series forecasting foundation model with 151 million parameters. Toto uses a modern decoder-only architecture coupled with architectural innovations designed to account for specific challenges found in multivariate observability time series data. Toto's pre-training corpus is a mixture of observability data, open datasets, and synthetic data, and is 4-10$\times$ larger than those of leading time series foundation models. Additionally, we introduce BOOM, a large-scale benchmark consisting of 350 million observations across 2,807 real-world time series. For both Toto and BOOM, we source observability data exclusively from Datadog's own telemetry and internal observability metrics. Extensive evaluations demonstrate that Toto achieves state-of-the-art performance on both BOOM and on established general purpose time series forecasting benchmarks. Toto's model weights, inference code, and evaluation scripts, as well as BOOM's data and evaluation code, are all available as open source under the Apache 2.0 License available at https://huggingface.co/Datadog/Toto-Open-Base-1.0 and https://github.com/DataDog/toto.

Ben Cohen
Emaad Khwaja
Youssef Doubli
Salahidine Lemaachi
Chris Lettieri
Charles Masson
Hugo Miccinilli
Elise Ramé
Qiqi Ren
Afshin Rostamizadeh
Jean Ogier du Terrail
Anna-Monica Toon
Kan Wang
Stephan Xie
Zongzhe Xu
Viktoriya Zhukova
David Asker
Ameet Talwalkar
Othmane Abou-Amal


Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting

Abstract: In deep time series forecasting, the Fourier Transform (FT) is extensively employed for frequency representation learning. However, it often struggles in capturing multi-scale, time-sensitive patterns. Although the Wavelet Transform (WT) can capture these patterns through frequency decomposition, its coefficients are insensitive to change points in time series, leading to suboptimal modeling. To mitigate these limitations, we introduce the multi-order Wavelet Derivative Transform (WDT) grounded in the WT, enabling the extraction of time-aware patterns spanning both the overall trend and subtle fluctuations. Compared with the standard FT and WT, which model the raw series, the WDT operates on the derivative of the series, selectively magnifying rate-of-change cues and exposing abrupt regime shifts that are particularly informative for time series modeling. Practically, we embed the WDT into a multi-branch framework named WaveTS, which decomposes the input series into multi-scale time-frequency coefficients, refines them via linear layers, and reconstructs them into the time domain via the inverse WDT. Extensive experiments on ten benchmark datasets demonstrate that WaveTS achieves state-of-the-art forecasting accuracy while retaining high computational efficiency.

Ziyu Zhou
Jiaxi Hu
Qingsong Wen
James T. Kwok
Yuxuan Liang


Foundation Time-Series AI Model for Realized Volatility Forecasting

Abstract: Time series foundation models (FMs) have emerged as a popular paradigm for zero-shot multi-domain forecasting. These models are trained on numerous diverse datasets and claim to be effective forecasters across multiple different time series domains, including financial data. In this study, we evaluate the effectiveness of FMs, specifically the TimesFM model, for volatility forecasting, a core task in financial risk management. We first evaluate TimesFM in its pretrained (zero-shot) form, followed by our custom fine-tuning procedure based on incremental learning, and compare the resulting models against standard econometric benchmarks. While the pretrained model provides a reasonable baseline, our findings show that incremental fine-tuning, which allows the model to adapt to new financial return data over time, is essential for learning volatility patterns effectively. Fine-tuned variants not only improve forecast accuracy but also statistically outperform traditional models, as demonstrated through Diebold-Mariano and Giacomini-White tests. These results highlight the potential of foundation models as scalable and adaptive tools for financial forecasting-capable of delivering strong performance in dynamic market environments when paired with targeted fine-tuning strategies.

Anubha Goel
Puneet Pasricha
Martin Magris
Juho Kanniainen


OLMA: One Loss for More Accurate Time Series Forecasting

Abstract: Time series forecasting faces two important but often overlooked challenges. Firstly, the inherent random noise in the time series labels sets a theoretical lower bound for the forecasting error, which is positively correlated with the entropy of the labels. Secondly, neural networks exhibit a frequency bias when modeling the state-space of time series, that is, the model performs well in learning certain frequency bands but poorly in others, thus restricting the overall forecasting performance. To address the first challenge, we prove a theorem that there exists a unitary transformation that can reduce the marginal entropy of multiple correlated Gaussian processes, thereby providing guidance for reducing the lower bound of forecasting error. Furthermore, experiments confirm that Discrete Fourier Transform (DFT) can reduce the entropy in the majority of scenarios. Correspondingly, to alleviate the frequency bias, we jointly introduce supervision in the frequency domain along the temporal dimension through DFT and Discrete Wavelet Transform (DWT). This supervision-side strategy is highly general and can be seamlessly integrated into any supervised learning method. Moreover, we propose a novel loss function named OLMA, which utilizes the frequency domain transformation across both channel and temporal dimensions to enhance forecasting. Finally, the experimental results on multiple datasets demonstrate the effectiveness of OLMA in addressing the above two challenges and the resulting improvement in forecasting accuracy. The results also indicate that the perspectives of entropy and frequency bias provide a new and feasible research direction for time series forecasting. The code is available at: https://github.com/Yuyun1011/OLMA-One-Loss-for-More-Accurate-Time-Series-Forecasting.

Tianyi Shi
Zhu Meng
Yue Chen
Siyang Zheng
Fei Su
Jin Huang
Changrui Ren
Zhicheng Zhao


Context-Aware Probabilistic Modeling with LLM for Multimodal Time Series Forecasting

Abstract: Time series forecasting is important for applications spanning energy markets, climate analysis, and traffic management. However, existing methods struggle to effectively integrate exogenous texts and align them with the probabilistic nature of large language models (LLMs). Current approaches either employ shallow text-time series fusion via basic prompts or rely on deterministic numerical decoding that conflict with LLMs' token-generation paradigm, which limits contextual awareness and distribution modeling. To address these limitations, we propose CAPTime, a context-aware probabilistic multimodal time series forecasting method that leverages text-informed abstraction and autoregressive LLM decoding. Our method first encodes temporal patterns using a pretrained time series encoder, then aligns them with textual contexts via learnable interactions to produce joint multimodal representations. By combining a mixture of distribution experts with frozen LLMs, we enable context-aware probabilistic forecasting while preserving LLMs' inherent distribution modeling capabilities. Experiments on diverse time series forecasting tasks demonstrate the superior accuracy and generalization of CAPTime, particularly in multimodal scenarios. Additional analysis highlights its robustness in data-scarce scenarios through hybrid probabilistic decoding.

Yueyang Yao
Jiajun Li
Xingyuan Dai
MengMeng Zhang
Xiaoyan Gong
Fei-Yue Wang
Yisheng Lv


OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domain

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

Wenzhen Yue
Yong Liu
Haoxuan Li
Hao Wang
Xianghua Ying
Ruohao Guo
Bowei Xing
Ji Shi


Adaptive Bayesian Very Short-Term Wind Power Forecasting Based on the Generalised Logit Transformation

Abstract: Wind power plays an increasingly significant role in achieving the 2050 Net Zero Strategy. Despite its rapid growth, its inherent variability presents challenges in forecasting. Accurately forecasting wind power generation is one key demand for the stable and controllable integration of renewable energy into existing grid operations. This paper proposes an adaptive method for very short-term forecasting that combines the generalised logit transformation with a Bayesian approach. The generalised logit transformation processes double-bounded wind power data to an unbounded domain, facilitating the application of Bayesian methods. A novel adaptive mechanism for updating the transformation shape parameter is introduced to leverage Bayesian updates by recovering a small sample of representative data. Four adaptive forecasting methods are investigated, evaluating their advantages and limitations through an extensive case study of over 100 wind farms ranging four years in the UK. The methods are evaluated using the Continuous Ranked Probability Score and we propose the use of functional reliability diagrams to assess calibration. Results indicate that the proposed Bayesian method with adaptive shape parameter updating outperforms benchmarks, yielding consistent improvements in CRPS and forecast reliability. The method effectively addresses uncertainty, ensuring robust and accurate probabilistic forecasting which is essential for grid integration and decision-making.

Tao Shen
Jethro Browell
Daniela Castro-Camilo


SCFormer: Structured Channel-wise Transformer with Cumulative Historical State for Multivariate Time Series Forecasting

Abstract: The Transformer model has shown strong performance in multivariate time series forecasting by leveraging channel-wise self-attention. However, this approach lacks temporal constraints when computing temporal features and does not utilize cumulative historical series effectively.To address these limitations, we propose the Structured Channel-wise Transformer with Cumulative Historical state (SCFormer). SCFormer introduces temporal constraints to all linear transformations, including the query, key, and value matrices, as well as the fully connected layers within the Transformer. Additionally, SCFormer employs High-order Polynomial Projection Operators (HiPPO) to deal with cumulative historical time series, allowing the model to incorporate information beyond the look-back window during prediction. Extensive experiments on multiple real-world datasets demonstrate that SCFormer significantly outperforms mainstream baselines, highlighting its effectiveness in enhancing time series forecasting. The code is publicly available at https://github.com/ShiweiGuo1995/SCFormer

Shiwei Guo
Ziang Chen
Yupeng Ma
Yunfei Han
Yi Wang

International Conference on Database Systems for Advanced Applications


Empirical Comparison of Lightweight Forecasting Models for Seasonal and Non-Seasonal Time Series

Abstract: Accurate time series forecasting is essential in many real-time applications that demand both high predictive accuracy and computational efficiency. This study provides an empirical comparison between a Polynomial Classifier and a Radial Basis Function Neural Network (RBFNN) across four real-world time series datasets (weather conditions, gold prices, crude oil prices, and beer production volumes) that cover both seasonal and nonseasonal patterns. Model performance is evaluated by forecasting accuracy (using Mean Absolute Error, Root Mean Squared Error, and Coefficient of Variation of Root Mean Squared Error) and computational time to assess each model's viability for real time forecasting. The results show that the PC yields more accurate and faster forecasts for non seasonal series, whereas the RBFNN performs better on series with pronounced seasonal patterns. From an interpretability standpoint, the polynomial model offers a simpler, more transparent structure (in contrast to the black box nature of neural network), which is advantageous for understanding and trust in real time decision making. The performance differences between PC and RBFNN are statistically significant, as confirmed by paired t tests and Wilcoxon signed rank tests. These findings provide practical guidance for model selection in time series forecasting, indicating that PC may be preferable for quick, interpretable forecasts in non-seasonal contexts, whereas RBFNN is superior for capturing complex seasonal behaviors

Thanh Son Nguyen
Dang Minh Duc Nguyen
Van Thanh Nguyen


Dual-Forecaster: A Multimodal Time Series Model Integrating Descriptive and Predictive Texts

Abstract: Most existing single-modal time series models rely solely on numerical series, which suffer from the limitations imposed by insufficient information. Recent studies have revealed that multimodal models can address the core issue by integrating textual information. However, these models focus on either historical or future textual information, overlooking the unique contributions each plays in time series forecasting. Besides, these models fail to grasp the intricate relationships between textual and time series data, constrained by their moderate capacity for multimodal comprehension. To tackle these challenges, we propose Dual-Forecaster, a pioneering multimodal time series model that combines both descriptively historical textual information and predictive textual insights, leveraging advanced multimodal comprehension capability empowered by three well-designed cross-modality alignment techniques. Our comprehensive evaluations on fifteen multimodal time series datasets demonstrate that Dual-Forecaster is a distinctly effective multimodal time series model that outperforms or is comparable to other state-of-the-art models, highlighting the superiority of integrating textual information for time series forecasting. This work opens new avenues in the integration of textual information with numerical time series data for multimodal time series analysis.

Wenfa Wu
Guanyu Zhang
Zheng Tan
Yi Wang
Hongsheng Qi


UniBiomed: A Universal Foundation Model for Grounded Biomedical Image Interpretation

Abstract: The integration of AI-assisted biomedical image analysis into clinical practice demands AI-generated findings that are not only accurate but also interpretable to clinicians. However, existing biomedical AI models generally lack the ability to simultaneously generate diagnostic findings and localize corresponding biomedical objects. This limitation makes it challenging for clinicians to correlate AI-generated findings with visual evidence (e.g., tiny lesions) in images and interpret the results of AI models. To address this challenge, we introduce UniBiomed, the first universal foundation model for grounded biomedical image interpretation, which is capable of generating accurate diagnostic findings and simultaneously segmenting the corresponding biomedical targets. UniBiomed is based on a novel integration of Multi-modal Large Language Model and Segment Anything Model, which can effectively unify diverse biomedical tasks in universal training for advancing grounded interpretation. To develop UniBiomed, we curate a large-scale dataset comprising over 27 million triplets of images, region annotations, and text descriptions across ten biomedical imaging modalities. Extensive validation on 70 internal and 14 external datasets demonstrated the state-of-the-art performance of UniBiomed in diverse biomedical tasks, including image segmentation, disease recognition, region-aware diagnosis, vision question answering, and report generation. In summary, UniBiomed is a powerful and versatile biomedical foundation model, unlocking the untapped grounded interpretation capability for optimizing AI-assisted biomedical image analysis.

Linshan Wu
Yuxiang Nie
Sunan He
Jiaxin Zhuang
Luyang Luo
Tao Li
Zhuoyao Xie
Dexuan Chen
Yinghua Zhao
Neeraj Mahboobani
Varut Vardhanabhuti
Ronald Cheong Kin Chan
Yifan Peng
Pranav Rajpurkar
Hao Chen


Evaluating Temporal Plasticity in Foundation Time Series Models for Incremental Fine-tuning

Abstract: Time series foundation models excel at diverse time series forecasting tasks, but their capacity for continuous improvement through incremental learning remains unexplored. We present the first comprehensive study investigating these models' temporal plasticity - their ability to progressively enhance performance through continual learning while maintaining existing capabilities. Through experiments on real-world datasets exhibiting distribution shifts, we evaluate both conventional deep learning models and foundation models using a novel continual learning framework. Our findings reveal that while traditional models struggle with performance deterioration during incremental fine-tuning, foundation models like Time-MoE and Chronos demonstrate sustained improvement in predictive accuracy. This suggests that optimizing foundation model fine-tuning strategies may be more valuable than developing domain-specific small models. Our research introduces new evaluation methodologies and insights for developing foundation time series models with robust continuous learning capabilities.

Jia Liu
Cheng Jinguo
Xia Fang
Zhenyuan Ma
Yuankai Wu


Bridging Distribution Gaps in Time Series Foundation Model Pretraining with Prototype-Guided Normalization

Abstract: Foundation models have achieved remarkable success across diverse machine-learning domains through large-scale pretraining on large, diverse datasets. However, pretraining on such datasets introduces significant challenges due to substantial mismatches in data distributions, a problem particularly pronounced with time series data. In this paper, we tackle this issue by proposing a domain-aware adaptive normalization strategy within the Transformer architecture. Specifically, we replace the traditional LayerNorm with a prototype-guided dynamic normalization mechanism (ProtoNorm), where learned prototypes encapsulate distinct data distributions, and sample-to-prototype affinity determines the appropriate normalization layer. This mechanism effectively captures the heterogeneity of time series characteristics, aligning pretrained representations with downstream tasks. Through comprehensive empirical evaluation, we demonstrate that our method significantly outperforms conventional pretraining techniques across both classification and forecasting tasks, while effectively mitigating the adverse effects of distribution shifts during pretraining. Incorporating ProtoNorm is as simple as replacing a single line of code. Extensive experiments on diverse real-world time series benchmarks validate the robustness and generalizability of our approach, advancing the development of more versatile time series foundation models.

Peiliang Gong
Emadeldeen Eldele
Min Wu
Zhenghua Chen
Xiaoli Li
Daoqiang Zhang

IEEE Transactions on Neural Networks and Learning Systems


Foundation Models for Time Series: A Survey

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

Siva Rama Krishna Kottapalli
Karthik Hubli
Sandeep Chandrashekhara
Garima Jain
Sunayana Hubli
Gayathri Botla
Ramesh Doddaiah


Integrating Quantum-Classical Attention in Patch Transformers for Enhanced Time Series Forecasting

Abstract: QCAAPatchTF is a quantum attention network integrated with an advanced patch-based transformer, designed for multivariate time series forecasting, classification, and anomaly detection. Leveraging quantum superpositions, entanglement, and variational quantum eigensolver principles, the model introduces a quantum-classical hybrid self-attention mechanism to capture multivariate correlations across time points. For multivariate long-term time series, the quantum self-attention mechanism can reduce computational complexity while maintaining temporal relationships. It then applies the quantum-classical hybrid self-attention mechanism alongside a feed-forward network in the encoder stage of the advanced patch-based transformer. While the feed-forward network learns nonlinear representations for each variable frame, the quantum self-attention mechanism processes individual series to enhance multivariate relationships. The advanced patch-based transformer computes the optimized patch length by dividing the sequence length into a fixed number of patches instead of using an arbitrary set of values. The stride is then set to half of the patch length to ensure efficient overlapping representations while maintaining temporal continuity. QCAAPatchTF achieves state-of-the-art performance in both long-term and short-term forecasting, classification, and anomaly detection tasks, demonstrating state-of-the-art accuracy and efficiency on complex real-world datasets.


Enhancing Time Series Forecasting with Fuzzy Attention-Integrated Transformers

Abstract: This paper introduces FANTF (Fuzzy Attention Network-Based Transformers), a novel approach that integrates fuzzy logic with existing transformer architectures to advance time series forecasting, classification, and anomaly detection tasks. FANTF leverages a proposed fuzzy attention mechanism incorporating fuzzy membership functions to handle uncertainty and imprecision in noisy and ambiguous time series data. The FANTF approach enhances its ability to capture complex temporal dependencies and multivariate relationships by embedding fuzzy logic principles into the self-attention module of the existing transformer's architecture. The framework combines fuzzy-enhanced attention with a set of benchmark existing transformer-based architectures to provide efficient predictions, classification and anomaly detection. Specifically, FANTF generates learnable fuzziness attention scores that highlight the relative importance of temporal features and data points, offering insights into its decision-making process. Experimental evaluatios on some real-world datasets reveal that FANTF significantly enhances the performance of forecasting, classification, and anomaly detection tasks over traditional transformer-based models.


CITRAS: Covariate-Informed Transformer for Time Series Forecasting

Abstract: In time series forecasting, covariates represent external factors that influence target variables. Some covariates are observable only in the past (observed covariates, such as recorded weather data), while others are known in advance (known covariates, such as calendar events or discount schedules). Although covariates have the potential to enhance forecasting performance, most deep learning-based forecasting models struggle to address the length discrepancy between variables caused by the future portion of known covariates and fail to leverage them flexibly. Moreover, capturing dependencies between target variables and covariates is non-trivial, as models must accurately reflect the local impact of covariates while simultaneously modeling global cross-variate dependencies. To address these challenges, we propose CITRAS, a decoder-only Transformer that flexibly integrates multiple target variables, observed covariates, and known covariates. While preserving strong autoregressive modeling capabilities, CITRAS introduces two novel mechanisms within patch-wise cross-variate attention: Key-Value (KV) Shift and Attention Score Smoothing. KV Shift seamlessly incorporates the future portion of known covariates into the forecasting process by aligning them with target variables based on their concurrent dependencies. Attention Score Smoothing refines locally accurate patch-wise cross-variate dependencies into global variate-level dependencies by smoothing the historical attention scores. Experimentally, CITRAS demonstrates strong performance across a wide range of real-world datasets in both covariate-informed and multivariate settings, showcasing its versatile ability to leverage cross-variate and cross-time dependencies for improved forecasting accuracy.

Yosuke Yamaguchi
Issei Suemitsu
Wenpeng Wei


Sentinel: Multi-Patch Transformer with Temporal and Channel Attention for Time Series Forecasting

Abstract: Transformer-based time series forecasting has recently gained strong interest due to the ability of transformers to model sequential data. Most of the state-of-the-art architectures exploit either temporal or inter-channel dependencies, limiting their effectiveness in multivariate time-series forecasting where both types of dependencies are crucial. We propose Sentinel, a full transformer-based architecture composed of an encoder able to extract contextual information from the channel dimension, and a decoder designed to capture causal relations and dependencies across the temporal dimension. Additionally, we introduce a multi-patch attention mechanism, which leverages the patching process to structure the input sequence in a way that can be naturally integrated into the transformer architecture, replacing the multi-head splitting process. Extensive experiments on standard benchmarks demonstrate that Sentinel, because of its ability to "monitor" both the temporal and the inter-channel dimension, achieves better or comparable performance with respect to state-of-the-art approaches.

Davide Villaboni
Alberto Castellini
Ivan Luciano Danesi
Alessandro Farinelli


A Note on Local Linear Regression for Time Series in Banach Spaces

Abstract: This work extends local linear regression to Banach space-valued time series for estimating smoothly varying means and their derivatives in non-stationary data. The asymptotic properties of both the standard and bias-reduced Jackknife estimators are analyzed under mild moment conditions, establishing their convergence rates. Simulation studies assess the finite sample performance of these estimators and compare them with the Nadaraya-Watson estimator. Additionally, the proposed methods are applied to smooth EEG recordings for reconstructing eye movements and to video analysis for detecting pedestrians and abandoned objects.


Realized Volatility Forecasting for New Issues and Spin-Offs using Multi-Source Transfer Learning

Abstract: Forecasting the volatility of financial assets is essential for various financial applications. This paper addresses the challenging task of forecasting the volatility of financial assets with limited historical data, such as new issues or spin-offs, by proposing a multi-source transfer learning approach. Specifically, we exploit complementary source data of assets with a substantial historical data record by selecting source time series instances that are most similar to the limited target data of the new issue/spin-off. Based on these instances and the target data, we estimate linear and non-linear realized volatility models and compare their forecasting performance to forecasts of models trained exclusively on the target data, and models trained on the entire source and target data. The results show that our transfer learning approach outperforms the alternative models and that the integration of complementary data is also beneficial immediately after the initial trading day of the new issue/spin-off.

Andreas Teller
Uta Pigorsch
Christian Pigorsch


Towards Efficient Large Scale Spatial-Temporal Time Series Forecasting via Improved Inverted Transformers

Abstract: Time series forecasting at scale presents significant challenges for modern prediction systems, particularly when dealing with large sets of synchronized series, such as in a global payment network. In such systems, three key challenges must be overcome for accurate and scalable predictions: 1) emergence of new entities, 2) disappearance of existing entities, and 3) the large number of entities present in the data. The recently proposed Inverted Transformer (iTransformer) architecture has shown promising results by effectively handling variable entities. However, its practical application in large-scale settings is limited by quadratic time and space complexity ($O(N^2)$) with respect to the number of entities $N$. In this paper, we introduce EiFormer, an improved inverted transformer architecture that maintains the adaptive capabilities of iTransformer while reducing computational complexity to linear scale ($O(N)$). Our key innovation lies in restructuring the attention mechanism to eliminate redundant computations without sacrificing model expressiveness. Additionally, we incorporate a random projection mechanism that not only enhances efficiency but also improves prediction accuracy through better feature representation. Extensive experiments on the public LargeST benchmark dataset and a proprietary large-scale time series dataset demonstrate that EiFormer significantly outperforms existing methods in both computational efficiency and forecasting accuracy. Our approach enables practical deployment of transformer-based forecasting in industrial applications where handling time series at scale is essential.

Jiarui Sun
Chin-Chia Michael Yeh
Yujie Fan
Xin Dai
Xiran Fan
Zhimeng Jiang
Uday Singh Saini
Vivian Lai
Junpeng Wang
Huiyuan Chen
Zhongfang Zhuang
Yan Zheng
Girish Chowdhary


Minimal Time Series Transformer

Abstract: Transformer is the state-of-the-art model for many natural language processing, computer vision, and audio analysis problems. Transformer effectively combines information from the past input and output samples in auto-regressive manner so that each sample becomes aware of all inputs and outputs. In sequence-to-sequence (Seq2Seq) modeling, the transformer processed samples become effective in predicting the next output. Time series forecasting is a Seq2Seq problem. The original architecture is defined for discrete input and output sequence tokens, but to adopt it for time series, the model must be adapted for continuous data. This work introduces minimal adaptations to make the original transformer architecture suitable for continuous value time series data.


LangTime: A Language-Guided Unified Model for Time Series Forecasting with Proximal Policy Optimization

Abstract: Recent research has shown an increasing interest in utilizing pre-trained large language models (LLMs) for a variety of time series applications. However, there are three main challenges when using LLMs as foundational models for time series forecasting: (1) Cross-domain generalization. (2) Cross-modality alignment. (3) Error accumulation in autoregressive frameworks. To address these challenges, we proposed LangTime, a language-guided unified model for time series forecasting that incorporates cross-domain pre-training with reinforcement learning-based fine-tuning. Specifically, LangTime constructs Temporal Comprehension Prompts (TCPs), which include dataset-wise and channel-wise instructions, to facilitate domain adaptation and condense time series into a single token, enabling LLMs to understand better and align temporal data. To improve autoregressive forecasting, we introduce TimePPO, a reinforcement learning-based fine-tuning algorithm. TimePPO mitigates error accumulation by leveraging a multidimensional rewards function tailored for time series and a repeat-based value estimation strategy. Extensive experiments demonstrate that LangTime achieves state-of-the-art cross-domain forecasting performance, while TimePPO fine-tuning effectively enhances the stability and accuracy of autoregressive forecasting.

Wenzhe Niu
Zongxia Xie
Yanru Sun
Wei He
Man Xu
Chao Hao


TimeFound: A Foundation Model for Time Series Forecasting

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

Congxi Xiao
Jingbo Zhou
Yixiong Xiao
Xinjiang Lu
Le Zhang
Hui Xiong


TS-RAG: Retrieval-Augmented Generation based Time Series Foundation Models are Stronger Zero-Shot Forecaster

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

Kanghui Ning
Zijie Pan
Yu Liu
Yushan Jiang
James Yiming Zhang
Kashif Rasul
Anderson Schneider
Lintao Ma
Yuriy Nevmyvaka
Dongjin Song


Unify and Anchor: A Context-Aware Transformer for Cross-Domain Time Series Forecasting

Abstract: The rise of foundation models has revolutionized natural language processing and computer vision, yet their best practices to time series forecasting remains underexplored. Existing time series foundation models often adopt methodologies from these fields without addressing the unique characteristics of time series data. In this paper, we identify two key challenges in cross-domain time series forecasting: the complexity of temporal patterns and semantic misalignment. To tackle these issues, we propose the ``Unify and Anchor" transfer paradigm, which disentangles frequency components for a unified perspective and incorporates external context as domain anchors for guided adaptation. Based on this framework, we introduce ContexTST, a Transformer-based model that employs a time series coordinator for structured representation and the Transformer blocks with a context-informed mixture-of-experts mechanism for effective cross-domain generalization. Extensive experiments demonstrate that ContexTST advances state-of-the-art forecasting performance while achieving strong zero-shot transferability across diverse domains.

Xiaobin Hong
Jiawen Zhang
Wenzhong Li
Sanglu Lu
Jia Li


Decision-Focused Fine-Tuning of Time Series Foundation Models for Dispatchable Feeder Optimization

Abstract: Time series foundation models provide a universal solution for generating forecasts to support optimization problems in energy systems. Those foundation models are typically trained in a prediction-focused manner to maximize forecast quality. In contrast, decision-focused learning directly improves the resulting value of the forecast in downstream optimization rather than merely maximizing forecasting quality. The practical integration of forecast values into forecasting models is challenging, particularly when addressing complex applications with diverse instances, such as buildings. This becomes even more complicated when instances possess specific characteristics that require instance-specific, tailored predictions to increase the forecast value. To tackle this challenge, we use decision-focused fine-tuning within time series foundation models to offer a scalable and efficient solution for decision-focused learning applied to the dispatchable feeder optimization problem. To obtain more robust predictions for scarce building data, we use Moirai as a state-of-the-art foundation model, which offers robust and generalized results with few-shot parameter-efficient fine-tuning. Comparing the decision-focused fine-tuned Moirai with a state-of-the-art classical prediction-focused fine-tuning Morai, we observe an improvement of 9.45% in average total daily costs.

Maximilian Beichter
Nils Friederich
Janik Pinter
Dorina Werling
Kaleb Phipps
Sebastian Beichter
Oliver Neumann
Ralf Mikut
Veit Hagenmeyer
Benedikt Heidrich


Dynamic Gradient Sparsification Training for Few-Shot Fine-tuning of CT Lymph Node Segmentation Foundation Model

Abstract: Accurate lymph node (LN) segmentation is critical in radiotherapy treatment and prognosis analysis, but is limited by the need for large annotated datasets. While deep learning-based segmentation foundation models show potential in developing high-performing models with fewer samples, their medical adaptation faces LN domain-specific prior deficiencies and inefficient few-shot fine-tuning for complex clinical practices, highlighting the necessity of an LN segmentation foundation model. In this work, we annotated 36,106 visible LNs from 3,346 publicly available head-and-neck CT scans to establish a robust LN segmentation model (nnUNetv2). Building on this, we propose Dynamic Gradient Sparsification Training (DGST), a few-shot fine-tuning approach that preserves foundational knowledge while dynamically updating the most critical parameters of the LN segmentation model with few annotations. We validate it on two publicly available LN segmentation datasets: SegRap2023 and LNQ2023. The results show that DGST outperforms existing few-shot fine-tuning methods, achieving satisfactory performance with limited labeled data. We release the dataset, models and all implementations to facilitate relevant research: https://github.com/Zihaoluoh/LN-Seg-FM.

Zihao Luo
Zijun Gao
Wenjun Liao
Shichuan Zhang
Guotai Wang
Xiangde Luo

International Conference on Medical Image Computing and Computer-Assisted Intervention


TimesBERT: A BERT-Style Foundation Model for Time Series Understanding

Abstract: Time series analysis is crucial in diverse scenarios. Beyond forecasting, considerable real-world tasks are categorized into classification, imputation, and anomaly detection, underscoring different capabilities termed time series understanding in this paper. While GPT-style models have been positioned as foundation models for time series forecasting, the BERT-style architecture, which has made significant advances in natural language understanding, has not been fully unlocked for time series understanding, possibly attributed to the undesirable dropout of essential elements of BERT. In this paper, inspired by the shared multi-granularity structure between multivariate time series and multisentence documents, we design TimesBERT to learn generic representations of time series including temporal patterns and variate-centric characteristics. In addition to a natural adaptation of masked modeling, we propose a parallel task of functional token prediction to embody vital multi-granularity structures. Our model is pre-trained on 260 billion time points across diverse domains. Leveraging multi-granularity representations, TimesBERT achieves state-of-the-art performance across four typical downstream understanding tasks, outperforming task-specific models and language pre-trained backbones, positioning it as a versatile foundation model for time series understanding.

Haoran Zhang
Yong Liu
Yunzhong Qiu
Haixuan Liu
Zhongyi Pei
Jianmin Wang
Mingsheng Long


PFformer: A Position-Free Transformer Variant for Extreme-Adaptive Multivariate Time Series Forecasting

Abstract: Multivariate time series (MTS) forecasting is vital in fields like weather, energy, and finance. However, despite deep learning advancements, traditional Transformer-based models often diminish the effect of crucial inter-variable relationships by singular token embedding and struggle to effectively capture complex dependencies among variables, especially in datasets with rare or extreme events. These events create significant imbalances and lead to high skewness, complicating accurate prediction efforts. This study introduces PFformer, a position-free Transformer-based model designed for single-target MTS forecasting, specifically for challenging datasets characterized by extreme variability. PFformer integrates two novel embedding strategies: Enhanced Feature-based Embedding (EFE) and Auto-Encoder-based Embedding (AEE). EFE effectively encodes inter-variable dependencies by mapping related sequence subsets to high-dimensional spaces without positional constraints, enhancing the encoder's functionality. PFformer shows superior forecasting accuracy without the traditional limitations of positional encoding in MTS modeling. We evaluated PFformer across four challenging datasets, focusing on two key forecasting scenarios: long sequence prediction for 3 days ahead and rolling predictions every four hours to reflect real-time decision-making processes in water management. PFformer demonstrated remarkable improvements, from 20% to 60%, compared with state-of-the-art models.

Pacific-Asia Conference on Knowledge Discovery and Data Mining


Forecasting intermittent time series with Gaussian Processes and Tweedie likelihood

Abstract: We adopt Gaussian Processes (GPs) as latent functions for probabilistic forecasting of intermittent time series. The model is trained in a Bayesian framework that accounts for the uncertainty about the latent function. We couple the latent GP variable with two types of forecast distributions: the negative binomial (NegBinGP) and the Tweedie distribution (TweedieGP). While the negative binomial has already been used in forecasting intermittent time series, this is the first time in which a fully parameterized Tweedie density is used for intermittent time series. We properly evaluate the Tweedie density, which has both a point mass at zero and heavy tails, avoiding simplifying assumptions made in existing models. We test our models on thousands of intermittent count time series. Results show that our models provide consistently better probabilistic forecasts than the competitors. In particular, TweedieGP obtains the best estimates of the highest quantiles, thus showing that it is more flexible than NegBinGP.

Stefano Damato
Dario Azzimonti
Giorgio Corani


TSKANMixer: Kolmogorov-Arnold Networks with MLP-Mixer Model for Time Series Forecasting

Abstract: Time series forecasting has long been a focus of research across diverse fields, including economics, energy, healthcare, and traffic management. Recent works have introduced innovative architectures for time series models, such as the Time-Series Mixer (TSMixer), which leverages multi-layer perceptrons (MLPs) to enhance prediction accuracy by effectively capturing both spatial and temporal dependencies within the data. In this paper, we investigate the capabilities of the Kolmogorov-Arnold Networks (KANs) for time-series forecasting by modifying TSMixer with a KAN layer (TSKANMixer). Experimental results demonstrate that TSKANMixer tends to improve prediction accuracy over the original TSMixer across multiple datasets, ranking among the top-performing models compared to other time series approaches. Our results show that the KANs are promising alternatives to improve the performance of time series forecasting by replacing or extending traditional MLPs.


Mantis: Lightweight Calibrated Foundation Model for User-Friendly Time Series Classification

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

Vasilii Feofanov
Songkang Wen
Marius Alonso
Romain Ilbert
Hongbo Guo
Malik Tiomoko
Lujia Pan
Jianfeng Zhang
Ievgen Redko


Learning Novel Transformer Architecture for Time-series Forecasting

Abstract: Despite the success of Transformer-based models in the time-series prediction (TSP) tasks, the existing Transformer architecture still face limitations and the literature lacks comprehensive explorations into alternative architectures. To address these challenges, we propose AutoFormer-TS, a novel framework that leverages a comprehensive search space for Transformer architectures tailored to TSP tasks. Our framework introduces a differentiable neural architecture search (DNAS) method, AB-DARTS, which improves upon existing DNAS approaches by enhancing the identification of optimal operations within the architecture. AutoFormer-TS systematically explores alternative attention mechanisms, activation functions, and encoding operations, moving beyond the traditional Transformer design. Extensive experiments demonstrate that AutoFormer-TS consistently outperforms state-of-the-art baselines across various TSP benchmarks, achieving superior forecasting accuracy while maintaining reasonable training efficiency.


Lightweight Online Adaption for Time Series Foundation Model Forecasts

Abstract: Foundation models (FMs) have emerged as a promising approach for time series forecasting. While effective, FMs typically remain fixed during deployment due to the high computational costs of learning them online. Consequently, deployed FMs fail to adapt their forecasts to current data characteristics, despite the availability of online feedback from newly arriving data. This raises the question of whether FM performance can be enhanced by the efficient usage of this feedback. We propose ELF to answer this question. ELF is a lightweight mechanism for the online adaption of FM forecasts in response to online feedback. ELF consists of two parts: a) the ELF-Forecaster which is used to learn the current data distribution; and b) the ELF-Weighter which is used to combine the forecasts of the FM and the ELF-Forecaster. We evaluate the performance of ELF in conjunction with several recent FMs across a suite of standard time series datasets. In all of our experiments we find that using ELF improves performance. This work demonstrates how efficient usage of online feedback can be used to improve FM forecasts.

Thomas L. Lee
William Toner
Rajkarn Singh
Artjom Joosen
Martin Asenov


S2TX: Cross-Attention Multi-Scale State-Space Transformer for Time Series Forecasting

Abstract: Time series forecasting has recently achieved significant progress with multi-scale models to address the heterogeneity between long and short range patterns. Despite their state-of-the-art performance, we identify two potential areas for improvement. First, the variates of the multivariate time series are processed independently. Moreover, the multi-scale (long and short range) representations are learned separately by two independent models without communication. In light of these concerns, we propose State Space Transformer with cross-attention (S2TX). S2TX employs a cross-attention mechanism to integrate a Mamba model for extracting long-range cross-variate context and a Transformer model with local window attention to capture short-range representations. By cross-attending to the global context, the Transformer model further facilitates variate-level interactions as well as local/global communications. Comprehensive experiments on seven classic long-short range time-series forecasting benchmark datasets demonstrate that S2TX can achieve highly robust SOTA results while maintaining a low memory footprint.

Zihao Wu
Juncheng Dong
Haoming Yang
Vahid Tarokh


Vision-Enhanced Time Series Forecasting via Latent Diffusion Models

Abstract: Diffusion models have recently emerged as powerful frameworks for generating high-quality images. While recent studies have explored their application to time series forecasting, these approaches face significant challenges in cross-modal modeling and transforming visual information effectively to capture temporal patterns. In this paper, we propose LDM4TS, a novel framework that leverages the powerful image reconstruction capabilities of latent diffusion models for vision-enhanced time series forecasting. Instead of introducing external visual data, we are the first to use complementary transformation techniques to convert time series into multi-view visual representations, allowing the model to exploit the rich feature extraction capabilities of the pre-trained vision encoder. Subsequently, these representations are reconstructed using a latent diffusion model with a cross-modal conditioning mechanism as well as a fusion module. Experimental results demonstrate that LDM4TS outperforms various specialized forecasting models for time series forecasting tasks.

Weilin Ruan
Siru Zhong
Haomin Wen
Yuxuan Liang


AdaPTS: Adapting Univariate Foundation Models to Probabilistic Multivariate Time Series Forecasting

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

Abdelhakim Benechehab
Vasilii Feofanov
Giuseppe Paolo
Albert Thomas
Maurizio Filippone
Balázs Kégl


Forecasting time series with constraints

Abstract: Time series forecasting presents unique challenges that limit the effectiveness of traditional machine learning algorithms. To address these limitations, various approaches have incorporated linear constraints into learning algorithms, such as generalized additive models and hierarchical forecasting. In this paper, we propose a unified framework for integrating and combining linear constraints in time series forecasting. Within this framework, we show that the exact minimizer of the constrained empirical risk can be computed efficiently using linear algebra alone. This approach allows for highly scalable implementations optimized for GPUs. We validate the proposed methodology through extensive benchmarking on real-world tasks, including electricity demand forecasting and tourism forecasting, achieving state-of-the-art performance.

Nathan Doumèche
Francis Bach
Éloi Bedek
Gérard Biau
Claire Boyer
Yannig Goude


Fine-Tuning Foundation Models with Federated Learning for Privacy Preserving Medical Time Series Forecasting

Abstract: Federated Learning (FL) provides a decentralized machine learning approach, where multiple devices or servers collaboratively train a model without sharing their raw data, thus enabling data privacy. This approach has gained significant interest in academia and industry due to its privacy-preserving properties, which are particularly valuable in the medical domain where data availability is often protected under strict regulations. A relatively unexplored area is the use of FL to fine-tune Foundation Models (FMs) for time series forecasting, potentially enhancing model efficacy by overcoming data limitation while maintaining privacy. In this paper, we fine-tuned time series FMs with Electrocardiogram (ECG) and Impedance Cardiography (ICG) data using different FL techniques. We then examined various scenarios and discussed the challenges FL faces under different data heterogeneity configurations. Our empirical results demonstrated that while FL can be effective for fine-tuning FMs on time series forecasting tasks, its benefits depend on the data distribution across clients. We highlighted the trade-offs in applying FL to FM fine-tuning.

Mahad Ali
Curtis Lisle
Patrick W. Moore
Tammer Barkouki
Brian J. Kirkwood
Laura J. Brattain

Annual International Conference of the IEEE Engineering in Medicine and Biology Society


HDT: Hierarchical Discrete Transformer for Multivariate Time Series Forecasting

Abstract: Generative models have gained significant attention in multivariate time series forecasting (MTS), particularly due to their ability to generate high-fidelity samples. Forecasting the probability distribution of multivariate time series is a challenging yet practical task. Although some recent attempts have been made to handle this task, two major challenges persist: 1) some existing generative methods underperform in high-dimensional multivariate time series forecasting, which is hard to scale to higher dimensions; 2) the inherent high-dimensional multivariate attributes constrain the forecasting lengths of existing generative models. In this paper, we point out that discrete token representations can model high-dimensional MTS with faster inference time, and forecasting the target with long-term trends of itself can extend the forecasting length with high accuracy. Motivated by this, we propose a vector quantized framework called Hierarchical Discrete Transformer (HDT) that models time series into discrete token representations with l2 normalization enhanced vector quantized strategy, in which we transform the MTS forecasting into discrete tokens generation. To address the limitations of generative models in long-term forecasting, we propose a hierarchical discrete Transformer. This model captures the discrete long-term trend of the target at the low level and leverages this trend as a condition to generate the discrete representation of the target at the high level that introduces the features of the target itself to extend the forecasting length in high-dimensional MTS. Extensive experiments on five popular MTS datasets verify the effectiveness of our proposed method.

Shibo Feng
Peilin Zhao
Liu Liu
Pengcheng Wu
Zhiqi Shen

AAAI Conference on Artificial Intelligence


Two-stage hybrid models for enhancing forecasting accuracy on heterogeneous time series

Abstract: A time series forecasting model--which is typically built on a single time series--is known as a local time series model (tsLM). In contrast, a forecasting model trained on multiple time series is referred to as a global time series model (tsGM). tsGMs can enhance forecasting accuracy and improve generalisation by learning cross-series information. As such, developing tsGMs has become a prominent research focus within the time series forecasting community. However, the benefits of tsGMs may not always be realised if the given set of time series is heterogeneous. While increasing model complexity can help tsGMs adapt to such a set of data, it can also increase the risk of overfitting and forecasting error. Additionally, the definition of homogeneity remains ambiguous in the literature. To address these challenges, this paper explores how to define data heterogeneity and proposes a two-stage modelling framework: At stage one, a tsGM is learnt to identify homogeneous patterns; and at stage two, tsLMs (e.g., ARIMA) or sub-tsGMs tailored to different groups are learnt to capture the heterogeneity. Numerical experiments on four open datasets demonstrate that the proposed approach significantly outperforms six state-of-the-art models. These results highlight its effectiveness in unlocking the full potential of global forecasting models for heterogeneous datasets.

European Conference on Artificial Intelligence


Transformers and Their Roles as Time Series Foundation Models

Abstract: We give a comprehensive analysis of transformers as time series foundation models, focusing on their approximation and generalization capabilities. First, we demonstrate that there exist transformers that fit an autoregressive model on input univariate time series via gradient descent. We then analyze MOIRAI, a multivariate time series foundation model capable of handling an arbitrary number of covariates. We prove that it is capable of automatically fitting autoregressive models with an arbitrary number of covariates, offering insights into its design and empirical success. For generalization, we establish bounds for pretraining when the data satisfies Dobrushin's condition. Experiments support our theoretical findings, highlighting the efficacy of transformers as time series foundation models.

Dennis Wu
Yihan He
Yuan Cao
Jianqing Fan
Han Liu


Benchmarking Time Series Forecasting Models: From Statistical Techniques to Foundation Models in Real-World Applications

Abstract: Time series forecasting is essential for operational intelligence in the hospitality industry, and particularly challenging in large-scale, distributed systems. This study evaluates the performance of statistical, machine learning (ML), deep learning, and foundation models in forecasting hourly sales over a 14-day horizon using real-world data from a network of thousands of restaurants across Germany. The forecasting solution includes features such as weather conditions, calendar events, and time-of-day patterns. Results demonstrate the strong performance of ML-based meta-models and highlight the emerging potential of foundation models like Chronos and TimesFM, which deliver competitive performance with minimal feature engineering, leveraging only the pre-trained model (zero-shot inference). Additionally, a hybrid PySpark-Pandas approach proves to be a robust solution for achieving horizontal scalability in large-scale deployments.


Sundial: A Family of Highly Capable Time Series Foundation Models

Abstract: We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on continuous-valued time series without discrete tokenization. Conditioned on arbitrary-length time series, our models are pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving more flexibility in representation learning than using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with one trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse via TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which achieve unprecedented model capacity and generalization performance. In addition to excellent scalability, Sundial achieves state-of-the-art results on both point and probabilistic forecasting benchmarks with a just-in-time inference speed, i.e., making zero-shot predictions within a few milliseconds. We believe that Sundial's pioneering generative forecasting capability can improve model reliability in real-world decision-making. Code is available at: https://github.com/thuml/Sundial.

Yong Liu
Guo Qin
Zhiyuan Shi
Zhi Chen
Caiyin Yang
Xiangdong Huang
Jianmin Wang
Mingsheng Long


Using Causality for Enhanced Prediction of Web Traffic Time Series

Abstract: Predicting web service traffic has significant social value, as it can be applied to various practical scenarios, including but not limited to dynamic resource scaling, load balancing, system anomaly detection, service-level agreement compliance, and fraud detection. Web service traffic is characterized by frequent and drastic fluctuations over time and are influenced by heterogeneous web user behaviors, making accurate prediction a challenging task. Previous research has extensively explored statistical approaches, and neural networks to mine features from preceding service traffic time series for prediction. However, these methods have largely overlooked the causal relationships between services. Drawing inspiration from causality in ecological systems, we empirically recognize the causal relationships between web services. To leverage these relationships for improved web service traffic prediction, we propose an effective neural network module, CCMPlus, designed to extract causal relationship features across services. This module can be seamlessly integrated with existing time series models to consistently enhance the performance of web service traffic predictions. We theoretically justify that the causal correlation matrix generated by the CCMPlus module captures causal relationships among services. Empirical results on real-world datasets from Microsoft Azure, Alibaba Group, and Ant Group confirm that our method surpasses state-of-the-art approaches in Mean Squared Error (MSE) and Mean Absolute Error (MAE) for predicting service traffic time series. These findings highlight the efficacy of leveraging causal relationships for improved predictions.

Chang Tian
Mingzhe Xing
Zenglin Shi
Matthew B. Blaschko
Yinliang Yue
Marie-Francine Moens


FreEformer: Frequency Enhanced Transformer for Multivariate Time Series Forecasting

Abstract: This paper presents \textbf{FreEformer}, a simple yet effective model that leverages a \textbf{Fre}quency \textbf{E}nhanced Trans\textbf{former} for multivariate time series forecasting. Our work is based on the assumption that the frequency spectrum provides a global perspective on the composition of series across various frequencies and is highly suitable for robust representation learning. Specifically, we first convert time series into the complex frequency domain using the Discrete Fourier Transform (DFT). The Transformer architecture is then applied to the frequency spectra to capture cross-variate dependencies, with the real and imaginary parts processed independently. However, we observe that the vanilla attention matrix exhibits a low-rank characteristic, thus limiting representation diversity. This could be attributed to the inherent sparsity of the frequency domain and the strong-value-focused nature of Softmax in vanilla attention. To address this, we enhance the vanilla attention mechanism by introducing an additional learnable matrix to the original attention matrix, followed by row-wise L1 normalization. Theoretical analysis~demonstrates that this enhanced attention mechanism improves both feature diversity and gradient flow. Extensive experiments demonstrate that FreEformer consistently outperforms state-of-the-art models on eighteen real-world benchmarks covering electricity, traffic, weather, healthcare and finance. Notably, the enhanced attention mechanism also consistently improves the performance of state-of-the-art Transformer-based forecasters.

Wenzhen Yue
Yong Liu
Xianghua Ying
Bowei Xing
Ruohao Guo
Ji Shi

International Joint Conference on Artificial Intelligence


Towards Lightweight Time Series Forecasting: a Patch-wise Transformer with Weak Data Enriching

Abstract: Patch-wise Transformer based time series forecasting achieves superior accuracy. However, this superiority relies heavily on intricate model design with massive parameters, rendering both training and inference expensive, thus preventing their deployments on edge devices with limited resources and low latency requirements. In addition, existing methods often work in an autoregressive manner, which take into account only historical values, but ignore valuable, easy-to-obtain context information, such as weather forecasts, date and time of day. To contend with the two limitations, we propose LiPFormer, a novel Lightweight Patch-wise Transformer with weak data enriching. First, to simplify the Transformer backbone, LiPFormer employs a novel lightweight cross-patch attention and a linear transformation-based attention to eliminate Layer Normalization and Feed Forward Network, two heavy components in existing Transformers. Second, we propose a lightweight, weak data enriching module to provide additional, valuable weak supervision to the training. It enhances forecasting accuracy without significantly increasing model complexity as it does not involve expensive, human-labeling but using easily accessible context information. This facilitates the weak data enriching to plug-and-play on existing models. Extensive experiments on nine benchmark time series datasets demonstrate that LiPFormer outperforms state-of-the-art methods in accuracy, while significantly reducing parameter scale, training duration, and GPU memory usage. Deployment on an edge device reveals that LiPFormer takes only 1/3 inference time compared to classic Transformers. In addition, we demonstrate that the weak data enriching can integrate seamlessly into various Transformer based models to enhance their accuracy, suggesting its generality.

Meng Wang
Jintao Yang
Bin Yang
Hui Li
Tongxin Gong
Bo Yang
Jiangtao Cui

IEEE International Conference on Data Engineering


Unveiling the Potential of Text in High-Dimensional Time Series Forecasting

Abstract: Time series forecasting has traditionally focused on univariate and multivariate numerical data, often overlooking the benefits of incorporating multimodal information, particularly textual data. In this paper, we propose a novel framework that integrates time series models with Large Language Models to improve high-dimensional time series forecasting. Inspired by multimodal models, our method combines time series and textual data in the dual-tower structure. This fusion of information creates a comprehensive representation, which is then processed through a linear layer to generate the final forecast. Extensive experiments demonstrate that incorporating text enhances high-dimensional time series forecasting performance. This work paves the way for further research in multimodal time series forecasting.

Xin Zhou
Weiqing Wang
Shilin Qu
Zhiqiang Zhang
Christoph Bergmeir