QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF CONDITIONAL AUTOREGRESSIVE WISHART MODELS

摘要

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.