Nonlinear Granger Causality Analysis Using Neural Network Architectures for Sequential Data

This work presents an analysis of nonlinear Granger causality (NNGC) computation based on artificial neural networks (ANN) architectures. The study evaluates the impact of using computational intelligence models as ANN, and how the training parameters can modify the causality estimation. For this, the employing from three chaotic maps (Henon, Ikeda, and Tinkerbell) and one neuron-like map (Rulkov) in bivariate scenarios were implemented. Three architectures from the ANN were used such as multilayer perceptron in a mode of the nonlinear autoregressive models, long-short memory term, and gated recurrent unit architectures were used to compute the NNGC, applying a forecasting on sequential data techniques. Results demonstrated that NNGC is highly sensitive to neural network parameters, such as the number of neurons, lag length, and batch size, with an optimal configuration by varying across chaotic maps. Comparisons with classical Granger causality were tested, revealing that neural networks effectively discover nonlinear relationships missed by linear methods, particularly in the Henon and Rulkov maps.