On the Markov-switching autoregressive stochastic volatility processes

• Ahmed Ghezal ^[1] ; Imane Zemmouri ^[2]
  1. [1] Department of Mathematics and Computer Sciences, Abdelhafid Boussouf University
  2. [2] Department of Mathematics, University of Annaba
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. 3, 2024, págs. 413-427
• Idioma: inglés
• DOI: 10.1007/s40324-023-00329-1
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• Resumen

  • Regime switching models are able to capture clustering effects, nonlinearities in time series and jumps in volatility. In the present paper, we propose a broad class of Markov-switching AutoRegressive Stochastic Volatility (MSAR − SV) models, in which the log−volatility follows a pth − MS−autoregression. So, it can be seen as a replacement of the general MS−GARCH model. This parameterization draws a lot of attention in modeling structural changes in dependent data. The parameters of the log− volatility are expressed as a function of a homogeneous Markov chain with a finite state space. The primary goal of the proposed model is to confer it a change driven by a Markov chain in order to capture by the habitual changing behavior of volatility due to economic forces, as the discrete shift in volatility due to abrupt abnormal events. Several probabilistic properties of MSAR−SV models have been obtained, especially, strictly (resp. second-order) stationary, causal and ergodic solution, geometric ergodicity, and computation of higher-order moments. Moreover, we derive the expression of the covariance function of the squared (resp. powers) process. Consequently, the logarithm squared (resp. powers) process admits an ARMA representation. Then we provide the limit theory for quasi-maximum likelihood estimator (QMLE), and, in addition, establish the strong consistency of this estimator. Finally, we present a simulation study on the performance of the proposed estimation method.