Granger Causality Detection in High-Dimensional Systems Using Feedforward Neural Networks

Abstract

This paper proposes a novel methodology to detect Granger causality in mean in vector autoregressive settings using feedforward neural networks. The approach accommodates unknown dependence structures between the elements of highly-dimensional multivariate time series with weak and strong persistence. To do this, we propose a two-stage procedure. First, we fit a neural network given by an optimal number of nodes in the intermediate hidden layers. This is done by maximising the transfer of information between input and output variables in the network. Second, we apply a novel sparse double group lasso penalty function to identify the variables that have predictive ability and, hence, Granger cause the others. The penalty function inducing sparsity is applied to the weights characterizing the nodes of the neural network. We show the correct identification of these weights for increasing sample sizes. A comprehensive simulation study shows the strong performance of our method for Granger causality detection in terms of size and power, and the consistency of the method for model selection for increasing sample sizes. An application to the recently created Tobalaba network of renewable energy companies shows the increase in connectivity between companies after the creation of the network using Granger-causality measures to map the connections.