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 considers some structural properties of Box-Cox transformed threshold GARCH(1,1) process. First, a sufficient and necessary condition for the strict stationarity of this threshold GARCH process is given. Second, some simple conditions for the existence of the moments of the threshold...

In order to capture three important dynamic characteristics of time series, the asymmetry, regimes, and conditional heteroskedasticity, based on Hwang and Basawa's [2004. Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes. Statist. Probab. Lett. 68, 209-220]...