A matrix approach to the Beveridge-Nelson decomposition of Markov-switching processes with applications to business cycle

ABSTRACT

We provide simple matrix formulas for calculation of the Beveridge–Nelson decomposition in the Markov-switching multivariate case, where series are generated by vector ARIMA models with Markov-switching intercept term. The treatment is immediately extended for regime changes in the mean, distributed lags in the regime and cointegrated models with Markov switching. We apply the method to real data from an example representative of recently industrialized economies and from a classical study on the US business cycle.

KEYWORDS:

• Beveridge-Nelson decomposition
• trend and cyclical components
• Markov-switching process
• impulse-response functions

JEL CLASSIFICATION:

• C32
• C82
• E32

Acknowledgments

The author would like to thank the Editor-in-Chief of the journal, Professor David Peel, and the anonymous reviewer for his/her valuable and constructive comments which improved the final version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

Work financially supported by FAR research grant (2019) of the University of Modena and Reggio Emilia, Italy.