Spectral representation and autocovariance structure of Markov switching DSGE models

Abstract

We investigate the L²-structure of Markov switching Dynamic Stochastic General Equilibrium (MS DSGE) models and derive conditions for strict and second-order stationarity. Then we determine the autocovariance function of the process driven by a stationary MS DSGE model and give a stable VARMA representation of it. It turns out that the autocovariance structure of the process coincides with that of a standard VARMA. Finally, we propose a method to derive the spectral density in a matrix closed-form of MS DSGE models. Our results relate with the works of Francq and Zakoian, Krolzig, Zhang and Stine. Numerical and empirical illustrations complete the article.

Keywords:

• Multivariate DSGE
• state-space models
• Markov chains
• changes in regime
• autocovariance structure
• spectral density function

AMS CLASSIFICATION:

• 62G07
• 62H05
• 62M05
• 62M10

Acknowledgments

Work financially supported by FAR research grant (2017) of the University of Modena and Reggio Emilia, Italy. We should like to thank the Editor in Chief of the journal, Professor Narayanaswamy Balakrishnan, and the anonymous referee for their constructive comments and very useful suggestions and remarks which were most valuable for improvement of the final version of the article.