Multi-scale hierarchical model for long-term time series forecasting

Long-term time series forecasting (LTSF) has become an urgent requirement in many applications, such as wind power supply planning. This is a highly challenging task because it requires considering both the complex frequency-domain and time-domain information in long-term time series simultaneously. However, existing work only considers potential patterns in a single domain (e.g., time or frequency domain), whereas a large amount of time-frequency domain information exists in real-world LTSFs. In this paper, we propose a multi-scale hierarchical network (MHNet) based on time-frequency decomposition to solve the above problem. MHNet first introduces a multi-scale hierarchical representation, extracting and learning features of time series in the time domain, and gradually builds up a global understanding and representation of the time series at different time scales, enabling the model to process time series over lengthy periods of time with lower computational complexity. Then, the robustness to noise is enhanced by employing a transformer that leverages frequency-enhanced decomposition to model global dependencies and integrates attention mechanisms in the frequency domain. Meanwhile, forecasting accuracy is further improved by designing a periodic trend decomposition module for multiple decompositions to reduce input-output fluctuations. Experiments on five real benchmark datasets show that the forecasting accuracy and computational efficiency of MHNet outperform state-of-the-art methods.