The problem of detecting nonlinearity in time series generated by a state-dependent autoregressive model. A simulation study

The aim of the paper is to try to measure, through a Monte Carlo experiment, nonlinearity in time series generated by a strictly stationary and uniformly ergodic state-dependent autoregressive process. The model under study is intrinsically nonlinear but the choice of parameters strongly impacts on the type of serial dependence making its identification complicated. For this reason, the paper exploits two statistical tests of independence and linearity in order to select the parameter values which ensure the joint rejection of both hypothesis. After that, our study uses two measures of nonlinear dependence in time series recently introduced in the literature, the auto-distance correlation function and the autodependence function, in order to identify nonlinearity induced by the proposed model.