QML Estimation of Asymmetric Markov Switching GARCH(p, q) Processes

Abstract

In this paper, I propose a natural extension of time-invariant coefficients threshold GARCH (TGARCH) processes to time-varying one, in which the associated volatility switch between different regimes due to dependency of its coefficients on unobservable (latent) time homogeneous Markov chain with finite state space (MS-TGARCH). These models are showed to be capable to capture some phenomena observed for most financial time series, among others, the asymmetric patterns, leverage effects, dependency without correlation and tail heaviness. So, some theoretical probabilistic properties of such models are discussed, in particular, we establish firstly necessary and sufficient conditions ensuring the strict stationarity and ergodicity for solution process of MS-TGARCH. Secondary, we extend the standard results for the limit theory of the popular quasi-maximum likelihood estimator (QMLE) for estimating the unknown parameters involved in model and we examine thus the strong consistency of such estimates. The finite-sample properties of QMLE are illustrated by a Monte Carlo study. Our proposed model is applied to model the exchange rates of the Algerian Dinar against the single European currency (Euro).

Keywords

MS-TGARCH model / Strict stationarity / Strong consistency