Multivariate sequence prediction for graph convolutional networks based on ESMD and transfer entropy

Multivariate time series modeling has been an important topic of interest for researchers in various fields. However, most of the existing methods focus on univariate forecasts and their historical values with little consideration of potential spatial dependencies among multiple variables. Multivariate time series forecasting can be naturally viewed from the perspective of a graph, where each variable can be considered as a node in the graph and they are interrelated through hidden dependencies. To this end, this paper proposes a multivariate time series forecasting graph neural network model based on multi-scale temporal feature extraction and attention mechanisms. Specifically, extremely symmetric modal decomposition is used to extract the time-domain features of multivariate time series at different time scales to form the node features of the graph; meanwhile, transfer entropy is computed to represent the adjacency matrix between nodes as a priori information, so as to identify the causal relationship between variables. In addition, a graph convolutional neural network is used to generate node embeddings containing rich spatial relationships. Finally, the temporal relationships of the node embeddings are established by FEDformer to enable multivariate time series forecasting. The effectiveness of the model is validated with real data from the power, climate and financial sectors.