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

Abstract

Abstract This paper proposes a novel methodology to detect Granger causality on average in vector autoregressive settings using feedforward neural networks. The approach accommodates unknown dependence structures between elements of high-dimensional multivariate time series with weak and strong persistence. To do this, we propose a two-stage procedure: first, we maximize the transfer of information between input and output variables in the network in order to obtain an optimal number of nodes in the intermediate hidden layers. Second, we apply a novel sparse double group lasso penalty function in order to identify the variables that have the predictive ability and, hence, indicate that Granger causality is present in the others. The penalty function inducing sparsity is applied to the weights that characterize the nodes of the neural network. We show the correct identification of these weights so as to increase sample sizes. We apply this method to the recently created Tobalaba network of renewable energy companies and show the increase in connectivity between companies after the creation of the network using Granger causality measures to map the connections.