We consider a multivariate Markov-switching GARCH model which allows for regime-specific volatility dynamics, leverage effects, and correlation structures. Stationarity conditions are derived, and consistency of the maximum likelihood estimator (MLE) is established under the assumption of...

This paper considers a new so-called autoregressive process with ARCH(1) errors driven by a hidden Markov chain, Xt+1=α(Δt+1)Xt+ηt+1β(Δt+1)+λ(Δt+1)Xt2,t∈N, where (ηt) is a sequence of independent and identically distributed standard normal random variables, and (Δt) is a Markov chain...

This article investigates some structural properties of the Markov-switching GARCH process introduced by Haas, Mittnik, and Paolella. First, a sufficient and necessary condition for the existence of the weakly stationary solution of the process is presented. The solution is weakly stationary,...

This paper investigates stationarity of the so-called integrated Markov-switching generalized autoregressive conditionally heteroskedastic (GARCH) process, which is an important subclass of the Markov-switching GARCH process introduced by Francq, Roussignol, and Zakoïan (2001, <italic>Journal of Time...</italic>

A natural generalization of the first-order GARCH processes family introduced in 1999 to allow for higher-order past errors and conditional variances on the current conditional variance equation is proposed. This new family of GARCH processes includes many well-known GARCH processes. A...