FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure
  Graph Perspective
Kun Yi Qi Zhang Wei Fan Hui He Liang Hu Pengyang Wang Ning An Longbing Cao Zhendong Niu
Multivariate time series (MTS) forecasting has shown great importance in
numerous industries. Current state-of-the-art graph neural network (GNN)-based
forecasting methods usually require both graph networks (e.g., GCN) and
temporal networks (e.g., LSTM) to capture inter-series (spatial) dynamics and
intra-series (temporal) dependencies, respectively. However, the uncertain
compatibility of the two networks puts an extra burden on handcrafted model
designs. Moreover, the separate spatial and temporal modeling naturally
violates the unified spatiotemporal inter-dependencies in real world, which
largely hinders the forecasting performance. To overcome these problems, we
explore an interesting direction of directly applying graph networks and
rethink MTS forecasting from a pure graph perspective. We first define a novel
data structure, hypervariate graph, which regards each series value (regardless
of variates or timestamps) as a graph node, and represents sliding windows as
space-time fully-connected graphs. This perspective considers spatiotemporal
dynamics unitedly and reformulates classic MTS forecasting into the predictions
on hypervariate graphs. Then, we propose a novel architecture Fourier Graph
Neural Network (FourierGNN) by stacking our proposed Fourier Graph Operator
(FGO) to perform matrix multiplications in Fourier space. FourierGNN
accommodates adequate expressiveness and achieves much lower complexity, which
can effectively and efficiently accomplish the forecasting. Besides, our
theoretical analysis reveals FGO's equivalence to graph convolutions in the
time domain, which further verifies the validity of FourierGNN. Extensive
experiments on seven datasets have demonstrated our superior performance with
higher efficiency and fewer parameters compared with state-of-the-art methods.