Estimation and asymptotics for vector autoregressive models with unit roots and Markov switching trends

We provide a formal definition of an M-state multivariate Markov switching (MS) trend, describe its asymptotic distribution, and consider vector autoregressive processes with MS trends which contain either unit roots or a stationary part. Then, we estimate the coefficients of such models via ordinary least squares (OLS), and determine the asymptotic distributions of OLS estimators in terms of functionals on a multivariate Brownian motion.