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Asymptotic Theory for Rotated Multivariate GARCH Models



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Asai, Manabu and Chang, Chia-Lin and McAleer, Michael and Laurent, Pauwels (2018) Asymptotic Theory for Rotated Multivariate GARCH Models. [ Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 27, 2018, ISSN: 2341-2356 ]

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In this paper, we derive the statistical properties of a two step approach to estimating multivariate GARCH rotated BEKK (RBEKK) models. By the definition of rotated BEKK, we estimate the unconditional covariance matrix in the first step in order to rotate observed variables to have the identity matrix for its sample covariance matrix. In the second step, we estimate the remaining parameters via maximizing the quasi-likelihood function. For this two step quasi-maximum likelihood (2sQML) estimator, we show consistency and asymptotic normality under weak conditions. While second-order moments are needed for consistency of the estimated unconditional covariance matrix, the existence of finite sixthorder moments are required for convergence of the second-order derivatives of the quasilog-likelihood function. We also show the relationship of the asymptotic distributions of the 2sQML estimator for the RBEKK model and the variance targeting (VT) QML 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 of the Diagonal BEKK and the Diagonal RBEKK models.

Item Type:Working Paper or Technical Report
Additional Information:

The authors are most grateful to Yoshi Baba for very helpful comments and suggestions. The first author acknowledges the financial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science, and the Australian Academy of Science. The second author thanks the Ministry of Science and Technology (MOST) for financial support. The third author is most grateful for the financial support of the Australian Research Council, Ministry of Science and Technology (MOST), Taiwan, and the Japan Society for the Promotion of Science.

Uncontrolled Keywords:BEKK, Rotated BEKK, Diagonal BEKK, Variance targeting, Multivariate GARCH, Consistency, Asymptotic normality.
Subjects:Sciences > Mathematics > Mathematical statistics
Sciences > Mathematics > Probabilities
JEL:C13, C32
Series Name:Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
ID Code:49568
Deposited On:16 Oct 2018 10:53
Last Modified:15 Feb 2022 09:10

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