Trend and cycle decomposition of Markov switching (co)integrated time series

In this paper we derive the Beveridge–Nelson (BN) decomposition and the state space representation for various multivariate (co)integrated time series subject to Markov switching in regime. Then we provide explicit expressions for the BN trend and cyclical components in terms of the matrices involved in the state space representation of the considered process. Our matrix expressions in closed form improve computational performance since they are readily programmable and greatly reduce the computational cost. Then we develop impulse-response function analysis and represent the BN trend component as a random walk. An empirical application on the world economy illustrates the feasibility of the proposed approach.