In this paper, we explore some probabilistic and statistical properties of constant conditional correlation (CCC) multivariate periodic GARCH models (CCC − PGARCH for short). These models which encompass some interesting classes having (locally) long memory property, play an outstanding role in modelling multivariate financial time series exhibiting certain heteroskedasticity. So, we give in the first part some basic structural properties of such models as conditions ensuring the existence of the strict stationary and geometric ergodic solution (in periodic sense). As a result, it is shown that the moments of some positive order for strictly stationary solution of CCC − PGARCH models are finite.Upon this finding, we focus in the second part on the quasi-maximum likelihood (QML) estimator for estimating the unknown parameters involved in the models. So we establish strong consistency and asymptotic normality (CAN) of CCC − PGARCH models.

中文翻译：

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多元周期CCC-GARCH模型的QML估计的渐近性质

在本文中，我们探索了恒定条件相关（CCC）多元周期GARCH模型（简称CCC - PGARCH）的概率和统计性质。这些模型包含一些具有（局部）长存储属性的有趣类，它们在建模表现出一定异方差性的多元财务时间序列方面发挥了杰出的作用。因此，在第一部分中，我们给出了这些模型的一些基本结构特性，例如条件，这些条件确保存在严格的平稳和几何遍历解（在周期意义上）。结果表明，CCC - PGARCH的严格平稳解具有某些正阶矩。基于此发现，我们在第二部分中重点关注拟最大似然（QML）估计器，用于估计模型中涉及的未知参数。因此，我们建立了CCC - PGARCH模型的强一致性和渐近正态性（CAN）。