A matrix approach to the Beveridge-Nelson decomposition of Markov-Switching processes with applications to business cycle

We provide simple matrix formulas for calculation of the Beveridge-Nelson decomposition in the Markov-switching multivariate case, where series are generated by vector ARIMA models with Markov-switching intercept term. The treatment is immediately extended for regime changes in the mean, distributed lags in the regime and cointegrated models with Markov switching. We apply the method to real data from an example representative of recently industrialized economies and from a classical study on US business cycle.