TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series

2026-02-19

AI Summary

This work addresses the challenge of distribution shift between training and testing in non-stationary time series forecasting by proposing a plug-and-play, time-invariant frequency-domain operator (TIFO). TIFO explicitly models cross-sample stationarity structures in the frequency domain for the first time, leveraging Fourier transforms to construct spectral representations and learning global stationarity-aware spectral weights that amplify stationary frequency components while suppressing non-stationary ones. This mechanism effectively mitigates distributional discrepancies. Designed with a universal plugin architecture, TIFO seamlessly integrates into existing forecasting models. Extensive experiments demonstrate its superiority, achieving top performance in 18 out of 28 settings and second place in 6 others. On the ETTm2 benchmark, it improves average MSE by 33.3% and 55.3% respectively, while reducing computational overhead by 60%–70%.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Temporal Planning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Nonstationary time series forecasting suffers from the distribution shift issue due to the different distributions that produce the training and test data. Existing methods attempt to alleviate the dependence by, e.g., removing low-order moments from each individual sample. These solutions fail to capture the underlying time-evolving structure across samples and do not model the complex time structure. In this paper, we aim to address the distribution shift in the frequency space by considering all possible time structures. To this end, we propose a Time-Invariant Frequency Operator (TIFO), which learns stationarity-aware weights over the frequency spectrum across the entire dataset. The weight representation highlights stationary frequency components while suppressing non-stationary ones, thereby mitigating the distribution shift issue in time series. To justify our method, we show that the Fourier transform of time series data implicitly induces eigen-decomposition in the frequency space. TIFO is a plug-and-play approach that can be seamlessly integrated into various forecasting models. Experiments demonstrate our method achieves 18 top-1 and 6 top-2 results out of 28 forecasting settings. Notably, it yields 33.3% and 55.3% improvements in average MSE on the ETTm2 dataset. In addition, TIFO reduces computational costs by 60% -70% compared to baseline methods, demonstrating strong scalability across diverse forecasting models.

Problem

• nonstationary time series
• distribution shift
• time series forecasting
• stationarity
• frequency space

Innovation

• Time-Invariant Frequency Operator
• Stationarity-Aware Representation
• Frequency Domain Learning
• Distribution Shift Mitigation
• Plug-and-Play Forecasting