Neural network for univariate and multivariate nonlinearity tests

This paper aims to introduce a multiple output artificial neural network as a tool for testing nonlinearity in multivariate time series. Unlike previous studies, we use weights from trained networks to determine the support space for defining random weights of nonlinear regressors and obtain greater power. Moreover, this paper uses two hidden layer neural networks for univariate and multivariate nonlinearity tests. Simulation results show that the proposed method is more powerful than the Terasvirta, Lin, and Granger test in most functional forms and more powerful than the Tsay test in some cases. Taking into account univariate and multivariate time series, the neural network approach is much more powerful than both these tests.