Consistency of Quasi-Maximum Likelihood Estimators for the Regime-Switching GARCH Model

Regime-switching GARCH (generalized autoregressive conditionally heteroscedastic) model incorporates the idea of Markov switching into the somehow restrictive GARCH model, which significantly extends GARCH models. However, the statistical inference for this model is rather difficult due to the dependence to the whole regime path. In this paper, we obtain the consistency of the quasi-maximum likelihood esti-mators, by transforming it to an infinite order ARCH model. Simulation studies to illustrate asymptotic behavior of the estimators and a mode