For the multivariate COGARCH process, we obtain explicit expressions for the second-order structure of the “squared returns” process observed on an equidistant grid. Based on this, we present a generalized method of moments estimator for its parameters. Under appropriate moment and strong mixing conditions, we show that the resulting estimator is consistent and asymptotically normal. Sufficient conditions for strong mixing, stationarity and identifiability of the model parameters are discussed in detail. We investigate the finite sample behavior of the estimator in a simulation study.

中文翻译：

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多元 COGARCH(1,1) 过程的基于矩的估计

对于多元 COGARCH 过程，我们获得了在等距网格上观察到的“平方收益”过程的二阶结构的显式表达式。基于此，我们提出了一种广义的矩估计参数方法。在适当的时刻和强混合条件下，我们证明了得到的估计量是一致的并且是渐近正态的。详细讨论了模型参数的强混合、平稳性和可识别性的充分条件。我们在模拟研究中研究了估计器的有限样本行为。