FFDFormer: A Fourier Decomposed Transformer with Inter-Intra Variable Fourier Dependencies for Multivariate Time Series Forecasting

Multivariate time series forecasting has been widely used in many fields such as finance, electricity, etc., Transformer still plays an important role in multivariate time series research. However, most of the previous studies focus on the changes of the same variable in the time dimension and do not link the interactions among multivariate variables, which will make the prediction results inaccurate; meanwhile, capturing and extracting the features of the series only in the time domain will also ignore some hidden information. Therefore, we propose a Fourier Decomposition Transformer model with intra-inter variable Fourier dependencies(FFDFormer), which introduces a Fourier multi-kernel decomposition module to extract the obvious fluctuating seasonal components in the frequency domain, and then captures the long-term trend through a moving average kernel to model the different patterns. In addition, the model performs inter- and intra-variate feature extraction and introduces Fourier attention to capture more comprehensive serial information in the frequency domain. We conduct extensive experiments on six large datasets and show that the FFDFormer framework outperforms most existing benchmark models in terms of performance.