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

TL;DR

TIFO introduces a frequency domain approach that learns stationary weights across datasets to improve nonstationary time series forecasting, effectively reducing distribution shift and computational costs.

Contribution

The paper proposes TIFO, a novel frequency operator that captures stationarity-aware features, enhancing forecasting accuracy and scalability in nonstationary time series.

Findings

Achieves 18 top-1 and 6 top-2 results out of 28 settings.

Yields 33.3% and 55.3% improvements in MSE on ETTm2.

Reduces computational costs by 60-70%.

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.