Goodness-of-fit tests for Markov Switching VAR models using spectral analysis

We consider a vector autoregressive (VAR) model subject to Markov Switching and present results for testing the fit of such a model and its capability to parametrize appropriately the covariance structure of the observed multivariate process. The proposed method is based on a linear VARMA representation of the Markov Switching VAR model, from which we derive a close-form formula for its spectral density matrix. Then we evaluate the closeness of the sample spectral density matrix of the observed process to the spectral density matrix of the fitted model. Our results relate with the nice work of Paparoditis (2000, 2005) on the class of linear VARMA models. Some applications to real life data are proposed in order to illustrate the behavior of spectral density functions, the goodness-of-fit tests and the feasibility of the approach.