文章基本信息

标题：Asymptotic and Finite Sample Properties for Multivariate Rotated GARCH Models
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作者：Manabu Asai ; Manabu Asai ; Manabu Asai 等
期刊名称：Econometrics
印刷版ISSN：2225-1146
出版年度：2021
卷号：9
期号：1
页码：21
DOI：10.3390/econometrics9020021
语种：English
出版社：MDPI, Open Access Journal
摘要：This paper derives the statistical properties of a two-step approach to estimating multivariate rotated GARCH-BEKK (RBEKK) models. From the definition of RBEKK, the unconditional covariance matrix is estimated in the first step to rotate the observed variables in order to have the identity matrix for its sample covariance matrix. In the second step, the remaining parameters are estimated by maximizing the quasi-log-likelihood function. For this two-step quasi-maximum likelihood (2sQML) estimator, this paper shows consistency and asymptotic normality under weak conditions. While second-order moments are needed for the consistency of the estimated unconditional covariance matrix, the existence of the finite sixth-order moments is required for the convergence of the second-order derivatives of the quasi-log-likelihood function. This paper also shows the relationship between the asymptotic distributions of the 2sQML estimator for the RBEKK model and variance targeting quasi-maximum likelihood estimator for the VT-BEKK model. Monte Carlo experiments show that the bias of the 2sQML estimator is negligible and that the appropriateness of the diagonal specification depends on the closeness to either the diagonal BEKK or the diagonal RBEKK models. An empirical analysis of the returns of stocks listed on the Dow Jones Industrial Average indicates that the choice of the diagonal BEKK or diagonal RBEKK models changes over time, but most of the differences between the two forecasts are negligible.