On an asymmetric multivariate stochastic difference volatility: structure and estimation

Omar Alzeley; Ahmed Ghezal; Omar Alzeley; Ahmed Ghezal

doi:10.3934/math.2024902

AIMS Mathematics

2024, Volume 9, Issue 7: 18528-18552. doi: 10.3934/math.2024902

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On an asymmetric multivariate stochastic difference volatility: structure and estimation

Omar Alzeley ^{1
,
,},
Ahmed Ghezal ²

1.
Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Saudi Arabia
2.
Department of Mathematics, University Center of Mila, Algeria

Received: 17 January 2024 Revised: 11 May 2024 Accepted: 20 May 2024 Published: 03 June 2024
MSC : 62F12, 62M10

In this study, we explored an asymmetric multivariate stochastic difference volatility model that extends various probabilistic and statistical properties previously discussed in the literature. We rigorously established that the model exhibits periodic stationarity and periodic ergodicity. Additionally, we delved into the robust consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE), providing a comprehensive analysis of its theoretical underpinnings. Finally, we demonstrated the practical applicability of our major findings through a series of pertinent applications. This work not only contributes to the existing body of knowledge on stochastic volatility modeling, but also opens new avenues for further research in this domain.
- periodicity,
- multivariate asymmetric GARCH,
- stationarity,
- asymptotic properties
Citation: Omar Alzeley, Ahmed Ghezal. On an asymmetric multivariate stochastic difference volatility: structure and estimation[J]. AIMS Mathematics, 2024, 9(7): 18528-18552. doi: 10.3934/math.2024902

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Abstract

In this study, we explored an asymmetric multivariate stochastic difference volatility model that extends various probabilistic and statistical properties previously discussed in the literature. We rigorously established that the model exhibits periodic stationarity and periodic ergodicity. Additionally, we delved into the robust consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE), providing a comprehensive analysis of its theoretical underpinnings. Finally, we demonstrated the practical applicability of our major findings through a series of pertinent applications. This work not only contributes to the existing body of knowledge on stochastic volatility modeling, but also opens new avenues for further research in this domain.

References

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