In this article, we consider a quasi‐maximum likelihood (QML) estimation of conditional autoregressive Wishart models, which generalize the conditional autoregressive Wishart models by not restricting the conditional distribution of covariances to follow the Wishart distribution. Strong consistency is established under the existence of the expectation of the log of the determinant. Sufficient conditions for asymptotic normality of the QML estimator are derived. Monte Carlo experiments show an inefficiency caused by using non‐Wishart distributions, which are negligible for the sample size T = 500. We use the daily covariance matrix of the returns of the Nikkei 225 index and its futures for the QML estimation of the conditional autoregressive Wishart model. The results indicate its appropriateness for the QML estimation.

中文翻译：

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条件自回归Wishart模型的拟最大似然估计

在本文中，我们考虑了条件自回归Wishart模型的准最大似然（QML）估计，它通过不限制协方差的条件分布遵循Wishart分布来推广条件自回归Wishart模型。在行列式对数期望的存在下建立强一致性。导出了QML估计量的渐近正态性的充分条件。蒙特卡洛实验表明，由于使用非维沙特分布引起的效率低下，对于样本量T可以忽略不计 =500。我们使用日经225指数及其期货的每日协方差矩阵来进行条件自回归Wishart模型的QML估计。结果表明其适用于QML估计。