WaveForM: Graph Enhanced Wavelet Learning for Long Sequence Forecasting of Multivariate Time Series

Multivariate time series (MTS) analysis and forecasting are crucial in many real-world applications, such as smart traffic management and weather forecasting. However, most existing work either focuses on short sequence forecasting or makes predictions predominantly with time domain features, which is not effective at removing noises with irregular frequencies in MTS. Therefore, we propose WAVEFORM, an end-to-end graph enhanced Wavelet learning framework for long sequence FORecasting of MTS. WaveForM first utilizes Discrete Wavelet Transform (DWT) to represent MTS in the wavelet domain, which captures both frequency and time domain features with a sound theoretical basis. To enable the effective learning in the wavelet domain, we further propose a graph constructor, which learns a global graph to represent the relationships between MTS variables, and graph-enhanced prediction modules, which utilize dilated convolution and graph convolution to capture the correlations between time series and predict the wavelet coefficients at different levels. Extensive experiments on five real-world forecasting datasets show that our model can achieve considerable performance improvement over different prediction lengths against the most competitive baseline of each dataset.