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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.

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