Validating Markov Switching VAR Through Spectral Representations

We develop a method to validate the use of Markov switching models in modelling time series subject to structural changes. Particularly, we consider multivariate autoregressive models subject to Markov switching and derive close-form formulae for the spectral density of such models, based on their autocovariance functions and stable representations. Within this framework, we check the capability of the model to capture the relative importance of highand low-frequency variability of the series. Numerical examples and applications to U.S. macroeconomic and financial data illustrate the behaviour at different frequencies.