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Non-stationarity is a fundamental challenge in multivariate long-term time series forecasting, often manifested as rapid changes in amplitude and phase. These variations lead to severe distribution shifts and consequently degrade predictive…

Machine Learning · Computer Science 2026-03-19 Yue Hu , Jialiang Tang , Siwei Yu , Baosheng Yu , Jing Zhang , Dacheng Tao

Time series forecasting has important applications in financial analysis, weather forecasting, and traffic management. However, existing deep learning models are limited in processing non-stationary time series data because they cannot…

Machine Learning · Computer Science 2025-05-13 Yuqi Xiong , Yang Wen

Despite the remarkable successes of general-purpose neural networks, such as MLPs and Transformers, we find that they exhibit notable shortcomings in modeling and reasoning about periodic phenomena, achieving only marginal performance…

Machine Learning · Computer Science 2025-10-28 Yihong Dong , Ge Li , Yongding Tao , Xue Jiang , Kechi Zhang , Jia Li , Jinliang Deng , Jing Su , Jun Zhang , Jingjing Xu

Recent normalization-based methods have shown great success in tackling the distribution shift issue, facilitating non-stationary time series forecasting. Since these methods operate in the time domain, they may fail to fully capture the…

Machine Learning · Statistics 2024-10-17 Xihao Piao , Zheng Chen , Yushun Dong , Yasuko Matsubara , Yasushi Sakurai

Forecasting non-stationary time series is a challenging task because their statistical properties often change over time, making it hard for deep models to generalize well. Instance-level normalization techniques can help address shifts in…

Machine Learning · Computer Science 2025-06-09 Junpeng Lin , Tian Lan , Bo Zhang , Ke Lin , Dandan Miao , Huiru He , Jiantao Ye , Chen Zhang , Yan-fu Li

Transformers have shown great power in time series forecasting due to their global-range modeling ability. However, their performance can degenerate terribly on non-stationary real-world data in which the joint distribution changes over…

Machine Learning · Computer Science 2023-11-27 Yong Liu , Haixu Wu , Jianmin Wang , Mingsheng Long

Non-stationarity is an intrinsic property of real-world time series and plays a crucial role in time series forecasting. Previous studies primarily adopt instance normalization to attenuate the non-stationarity of original series for better…

Machine Learning · Computer Science 2025-03-05 Tianyu Jia , Zongxia Xie , Yanru Sun , Dilfira Kudrat , Qinghua Hu

Time series forecasting is critical for decision-making across dynamic domains such as energy, finance, transportation, and cloud computing. However, real-world time series often exhibit non-stationarity, including temporal distribution…

Machine Learning · Computer Science 2025-12-01 Junkai Lu , Peng Chen , Chenjuan Guo , Yang Shu , Meng Wang , Bin Yang

Time series forecasting presents significant challenges in real-world applications across various domains. Building upon the decomposition of the time series, we enhance the architecture of machine learning models for better multivariate…

Machine Learning · Computer Science 2026-02-24 Sanjeev Panta , Xu Yuan , Li Chen , Nian-Feng Tzeng

Due to the non-stationarity of time series, the distribution shift problem largely hinders the performance of time series forecasting. Existing solutions either rely on using certain statistics to specify the shift, or developing specific…

Machine Learning · Computer Science 2025-02-10 Wei Fan , Shun Zheng , Pengyang Wang , Rui Xie , Kun Yi , Qi Zhang , Jiang Bian , Yanjie Fu

Long-term time series forecasting is a long-standing challenge in various applications. A central issue in time series forecasting is that methods should expressively capture long-term dependency. Furthermore, time series forecasting…

Machine Learning · Computer Science 2024-11-06 Xingyu Zhang , Siyu Zhao , Zeen Song , Huijie Guo , Jianqi Zhang , Changwen Zheng , Wenwen Qiang

This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…

Classical Analysis and ODEs · Mathematics 2024-06-19 Pierre Warion , Bruno Torrésani

Reversible Instance Normalization (RevIN) is a key technique enabling simple linear models to achieve state-of-the-art performance in time series forecasting. While replacing its non-robust statistics with robust counterparts (termed…

Machine Learning · Computer Science 2025-10-07 Fanzhe Fu , Yang Yang

The synchrosqueezing transform, a kind of reassignment method, aims to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. In this paper, we consider the short-time Fourier…

Signal Processing · Electrical Eng. & Systems 2019-09-27 Lin Li , Haiyan Cai , Hongxia Han , Qingtang Jiang , Hongbing Ji

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.…

Machine Learning · Computer Science 2025-04-02 Sanjay Chakraborty , Fredrik Heintz

The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…

Machine Learning · Computer Science 2025-08-05 Runze Yang , Longbing Cao , Xin You , Kun Fang , Jianxun Li , Jie Yang

The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum. Practitioners seeking low-dimensional summary measures…

Methodology · Statistics 2021-03-12 Pramita Bagchi , Scott A. Bruce

We introduce a model-agnostic forward diffusion process for time-series forecasting that decomposes signals into spectral components, preserving structured temporal patterns such as seasonality more effectively than standard diffusion.…

Machine Learning · Statistics 2026-02-17 Francisco Caldas , Sahil Kumar , Cláudia Soares

Meta-forecasting is a newly emerging field which combines meta-learning and time series forecasting. The goal of meta-forecasting is to train over a collection of source time series and generalize to new time series one-at-a-time. Previous…

Machine Learning · Computer Science 2023-02-07 Mike Van Ness , Huibin Shen , Hao Wang , Xiaoyong Jin , Danielle C. Maddix , Karthick Gopalswamy

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

Dynamical Systems · Mathematics 2024-03-25 Anna Fitzpatrick , Molly Folino , Andrea Arnold
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