Deep Frequency Derivative Learning for Non-stationary Time Series Forecasting

Abstract

While most time series are non-stationary, it is inevitable for models to face the distribution shift issue in time series forecasting. Existing solutions manipulate statistical measures (usually mean and std.) to adjust time series distribution. However, these operations can be theoretically seen as the transformation towards zero frequency component of the spectrum which cannot reveal full distribution information and would further lead to information utilization bottleneck in normalization, thus hindering forecasting performance. To address this problem, we propose to utilize the whole frequency spectrum to transform time series to make full use of data distribution from the frequency perspective. We present a deep frequency derivative learning framework, DERITS, for non-stationary time series forecasting. Specifically, DERITS is built upon a novel reversible transformation, namely Frequency Derivative Transformation (FDT) that makes signals derived in the frequency domain to acquire more stationary frequency representations. Then, we propose the Order-adaptive Fourier Convolution Network to conduct adaptive frequency filtering and learning. Furthermore, we organize DERITS as a parallel-stacked architecture for the multi-order derivation and fusion for forecasting. Finally, we conduct extensive experiments on several datasets which show the consistent superiority in both time series forecasting and shift alleviation.