Measuring Frequency Non-Stationarity for Robust Time Series Forecasting

Rui LIANG, Lingwei Zhu, Xihao Piao, Yang Deng, Dong Wang, Junjie Chen, Dan Wang, Zheng Chen

Keywords: time series forecasting, deep learning

Abstract:

Non-stationarity in time series has long posed a fundamental challenge for forecasting models, as it leads to distribution shifts between training and test data.
A popular line of research, known as normalization methods, aims to measure and suppress non-stationarity by removing time-domain low-order statistics.
Nevertheless, low-order statistics may inadequately address the underlying non-stationary structures manifested as a composition of frequencies.
To tackle these issues,
we propose to measure the degree of stationarity of each frequency component across distributions via spectral analysis.
By identifying and downweighting frequencies that are more non-stationary, we re-represent the original time series to reduce distributional discrepancies between training and test sets.
Concretely, we present Fremen with threefold contributions.
Theoretically, Fremen is grounded in a principled formulation and we provide the first spectral analysis to support its validity.
Technically, Fremen is both novel and effective, incurring negligible additional computational cost.
Experimentally, Fremen is validated on four forecasting models across seven datasets, achieving 24 best results out of 28 settings and 28.4\% average MSE improvements.
Our code is publicly available at https://anonymous.4open.science/r/Fremen-code-82C8.

Primary Area: learning on time series and dynamical systems

Submission Number: 23679