Copula parameter change test for nonlinear AR models with nonlinear GARCH errors

In this paper, we study the problem of testing for a copula parameter change in nonlinear autoregressive (AR) models with nonlinear generalized autoregressive conditional heteroskedasticity (GARCH) errors. To perform a test, we propose the cusum test based on pseudo maximum likelihood estimates of copula parameters. We derive its limiting null distribution under regularity conditions. For illustration, we conduct a simulation study with an emphasis on STAR-STGARCH models. A real data analysis applied to the S&P 500 index and IBM stock price is also considered.