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 $(\mathrm{MS})$ trend, describe its asymptotic distribution, and consider vector autoregressive processes with $\mathrm{MS}$ trends which contain either unit roots or a stationary part. Then, we estimate the coefficients of such models via ordinary least squares $(\mathrm{OLS})$, and determine the asymptotic distributions of $\mathrm{OLS}$ estimators in terms of functionals on a multivariate Brownian motion.

Keywords:

• Markov chain
• Markov switching VAR model
• Markov switching trend
• unit root
• OLS estimator
• asymptotic distribution
• Brownian motion

JEL CLASSIFICATIONS:

• C01
• C05
• C32

Mathematics Subject Classifications:

• 62F12
• 62M05
• 62H10
• 62H12

Acknowledgments

The author is very grateful to the Editor in Chief, Professor Saul Jacka, the anonymous Associate Editor (who coordinated the review of the paper) and two anonymous referees for their very useful suggestions and remarks which improved the final version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is financially supported by a research grant (FAR 2022) of the University of Modena and Reggio E., Italy.