TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series
This addresses distribution shift issues in time series forecasting for applications requiring accurate predictions, though it is an incremental improvement as it builds on existing frequency-based methods.
The paper tackles the problem of distribution shift in nonstationary time series forecasting by proposing a Time-Invariant Frequency Operator (TIFO) that learns stationarity-aware weights over the frequency spectrum, resulting in top performance in 24 out of 28 forecasting settings, with improvements of 33.3% and 55.3% in average MSE on the ETTm2 dataset and computational cost reductions of 60%-70%.
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.