Markov Switching Normal-Mixture GARCH

ETUDE INTERNE
AUTEURS : ADRIEN MISKO, BAYE MATAR KANDJI

We introduce a volatility model in which the conditional volatility is driven by both a Markov switching (MS) sequence and innovations with normal mixture (NM) distributions, called MS-NM-GARCH. The existence of a strictly stationary solution and a second-order stationary solution is discussed. We use the likelihood approach to estimate the parameters of the model and, to our knowledge, establish for the first time the strong consistency of the maximum likelihood estimator (MLE) of a class of MS-GARCH under standard regular conditions. We develop an iterative algorithm based on the Hamilton filter and the Expectation Maximization algorithm to efficiently compute the MLE. Finally, we test our model to real financial data, showcasing its practical relevance.