  The key problem in multivariate time series (MTS) analysis and forecasting
aims to disclose the underlying couplings between variables that drive the
co-movements. Considerable recent successful MTS methods are built with graph
neural networks (GNNs) due to their essential capacity for relational modeling.
However, previous work often used a static graph structure of time-series
variables for modeling MTS failing to capture their ever-changing correlations
over time. To this end, a fully-connected supra-graph connecting any two
variables at any two timestamps is adaptively learned to capture the
high-resolution variable dependencies via an efficient graph convolutional
network. Specifically, we construct the Edge-Varying Fourier Graph Networks
(EV-FGN) equipped with Fourier Graph Shift Operator (FGSO) which efficiently
performs graph convolution in the frequency domain. As a result, a
high-efficiency scale-free parameter learning scheme is derived for MTS
analysis and forecasting according to the convolution theorem. Extensive
experiments show that EV-FGN outperforms state-of-the-art methods on seven
real-world MTS datasets.
