Multivariate time series forecasting based on fractional Fourier transforms

Multivariate time series forecasting has a large number of applications in the fields of meteorology, investment, and energy. Transformer-based prediction models have achieved good performance, but their computation of global correlation is responsible for a high degree, and they cannot effectively model local features like convolutional neural network(CNN) structures. As for the multi-scale dependency aspect, current research focuses on learning at fixed scales, including the dependency in time and frequency domains, and we hope that the model can automatically learn the appropriate scale features. In this paper, we propose a prediction model based on fractional Fourier transform, which decomposes the sequence, projects the data to different fractional domains using fractional Fourier transform, learns different global features, and can effectively obtain unconstrained scale dependence, and realizes cross-scale feature extraction, and fully learns the potential features in the sequence, and for the local information we utilize convolution to extract them, and the proposed model is called Fractional Fourier Convolutional Network (FRCNet). We have conducted extensive experiments on several publicly available datasets, including electricity, diseases, and exchange rates. The experimental results show strong competitiveness in multivariate time series forecasting.