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

Abstract

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