Title: TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series
Primary area: learning on time series and dynamical systems
Keywords: time series, deep learning

Abstract: Nonstationary time series forecasting suffers from the distribution shift issue due to the different distributions that produce the training and test data. 
The distributions can be regarded as governed by a time structure which itself may be subject to some probabilistic law.
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.
Learning the data-specific eigenvalues has the natural interpretation of weighting up frequency components responsible for distributional discrepancies.
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.