A Doubly Markov Switching Ar Model: Some Probabilistic Properties and Strong Consistency

Ghezal, Ahmed

doi:10.1007/s10958-023-06262-y

Cited by 8 publications

(1 citation statement)

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“…So some locally (i.e., in each "regime") linear or nonlinear representations were investigated in order to capture the probabilistic and statistical properties of such models. For instance, M S − ARM A: Francq and Zakoïan [10] and Stelzer [26]; M S−nonlinear ARM A : Lee [21] and Yao; M S − GARCH: Francq and Zakoïan [9]; Hass et al, [16]; Liu [22]; M S − DAR : Ghezal [14] among others. The M S − BLGARCH model generate series with a much more flexible dependence structure than in standard BLGARCH specifications proposed by Storti and Vitale (c.f., [27]) is a generalization of the classical M S − GARCH model studied by Cai (c.f., [3]), Hamilton and Susmel (c.f., [18]) and Francq et al (c.f., [11]), thereby explain the presence of leverage effects in the volatility dynamics.…”

Section: Introductionmentioning

confidence: 99%

Estimating MS-BLGARCH Models Using Recursive Method

Ghezal

Zemmouri²

2023

Pan-Amer. J. Math.

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In this paper a new class of models is proposed for modeling nonlinear and stationary time series. This new class of models is referred to as the Markov-switching bilinear GARCH (MS-BLGARCH) models. In these models, the parameters are allowed to depend on an unobservable time-homogeneous and stationary Markov chain with finite state space. The statistical inference for these models is rather difficult due to the dependence on the whole regime path. We propose a recursive algorithm for parameter estimation in MS − BLGARCH. The proposed method is useful for long time series as well as for data available in real time. The main idea is to use the maximum likelihood estimation (MLE) method and from this develop a recursive Expectation-Maximization (EM) algorithm.

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