Markov Switching Garch Models: Higher Order Moments, Kurtosis Measures, and Volatility Evaluation in Recessions and Pandemic

Abstract

In this article, we derive neat matrix formulas in closed form for computing higher order moments and kurtosis of univariate Markov switching GARCH models. Then we provide asymptotic theory for sample estimators of higher order moments and kurtosis which can be used for testing normality. We also check our theory statements numerically via Monte Carlo simulations. Finally, we take advantage of our theoretical results to recognize different periods of high volatility stressing the stock markets, such as financial crisis and pandemic.

Keywords:

• GARCH
• Geometric ergodicity
• Higher order moments
• Kurtosis measures
• Markov switching
• Stationarity
• Testing for normality
• Volatility indices

Acknowledgments

We thank the editor in chief of the journal, Professor Jianqing Fan, the associate editor, and the two anonymous referees for their constructive comments and very useful suggestions and remarks which were most valuable for improvement of the final version of the article.

Additional information

Funding

This work was financially supported by FAR (2020) research grant of the University of Modena and Reggio E., Italy.