The functional central limit theorem for the multivariate MS-ARMA-GARCH model

•A multivariate (ARMA)-GARCH model governed by Markov switching coefficients is considered.•Sufficient conditions for strict and second-order stationary of the process are given.•Sufficient conditions for the L2-NED property of the process are given.•The functional central limit theorem for the process is proved.

In this paper, we consider the multivariate ARMA-GARCH process governed by Markov switching coefficients. We show under proper assumptions that the process holds the L2-NED property and obeys the multivariate functional central limit theorem. The multivariate Markov switching constant conditional correlation(CCC)-GARCH model is considered as a special case.