Wavelet Transformer: An Effective Method on Multiple Periodic Decomposition for Time Series Forecasting

Time series forecasting has attracted significant interest across various fields in recent years. Notably, Transformers have been extensively investigated for long-term time series forecasting (LTSF) due to their remarkable ability on modeling sequential data. However, the point-wise calculation of its self-attention leads to a challenging task for accurately capturing real-world time series' local and global characteristics, especially with multiple seasonal periodic components and outliers. In this article, we leverage wavelet analysis to recognize different frequency patterns and design an effective attention mechanism for time series forecasting to address this issue. In detail, we employ the maximal overlap discrete wavelet transform (MODWT) to construct a novel wavelet attention (WA) mechanism and propose the wavelet transformer (Waveformer) prediction technique. This approach effectively extracts multiple periodic features, mitigates the influence of anomalies and improves the precision of time series prediction under seasonal-trend decomposition methods. Experimental evaluations on six real-world datasets from various application fields demonstrate that the multiple periodic decomposition strategy of Waveformer successfully captures time series seasonal patterns and improves forecasting performance in comparison with many state-of-art methods.