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.
Estimation and asymptotics for vector autoregressive models with unit roots and Markov switching trends / Cavicchioli, Maddalena. - In: STOCHASTICS. - ISSN 1744-2508. - 95:8(2023), pp. 1488-1509. [10.1080/17442508.2023.2227752]
Estimation and asymptotics for vector autoregressive models with unit roots and Markov switching trends
Cavicchioli, Maddalena
2023
Abstract
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.
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