Bridging self-attention and time series decomposition for periodic forecasting

In this paper, we study how to capture explicit periodicity to boost the accuracy of deep models in univariate time series forecasting. Recent advanced deep learning models such as recurrent neural networks (RNNs) and transformers have reached new heights in terms of modeling sequential data, such as natural languages, due to their powerful expressiveness. However, real-world time series are often more periodic than general sequential data, while recent studies confirm that standard neural networks are not capable of capturing the periodicity sufficiently because they have no modules that can represent periodicity explicitly. In this paper, we alleviate this challenge by bridging the self-attention network with time series decomposition and propose a novel framework called DeepFS. DeepFS equips Deep models with Fourier Series to preserve the periodicity of time series. Specifically, our model first uses self-attention to encode temporal patterns, from which to predict the periodic and non-periodic components for reconstructing the forecast outputs. The Fourier series is injected as an inductive bias in the periodic component. Capturing periodicity not only boosts the forecasting accuracy but also offers interpretable insights for real-world time series. Extensive empirical analyses on both synthetic and real-world datasets demonstrate the effectiveness of DeepFS. Studies about why and when DeepFS works provide further understanding of our model.