Forecasting Markov switching vector autoregressions: Evidence from simulation and application

Abstract

We derive the optimal forecasts for multivariate autoregressive time series processes subject to Markov switching in regime. Optimality means that the trace of the mean square forecast error matrix is minimized by using suitable weighting observations. Then we provide neat analytic expressions for the optimal weights in terms of the matrices involved in a state space representation of the considered process. Our matrix expressions in closed form improve computational performance since they are readily programmable. Numerical simulations and an empirical application illustrate the feasibility of the proposed approach. We provide evidence that the forecasts using optimal weights increase forecast precision and are more accurate than the traditional Markov switching alternatives.