Template-Type: ReDIF-Paper 1.0
Author-Name: Asai, M.
Author-Name-Last: Asai
Author-Name-First: Manabu
Author-Person: pas73
Author-Name: Chang, C-L.
Author-Name-Last: Chang
Author-Name-First: Chia-Lin
Author-Person: pch286
Author-Name: McAleer, M.J.
Author-Name-Last: McAleer
Author-Name-First: Michael
Author-Person: pmc90
Author-Name: Pauwels, L.
Author-Name-Last: Pauwels
Author-Name-First: Laurent
Title: Asymptotic Theory for Rotated Multivariate GARCH Models
Abstract: In this paper, we derive the statistical properties of a two step approach to estimating
 multivariate GARCH rotated BEKK (RBEKK) models. By the denition of rotated BEKK,
 we estimate the unconditional covariance matrix in the rst 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 nite sixth-order moments are
 required for convergence of the second-order derivatives of the quasi-log-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 specication depends on the closeness to either of the
 Diagonal BEKK and the Diagonal RBEKK models.
Length: 29
Creation-Date: 2018-10-01
File-URL: https://repub.eur.nl/pub/111553/EI2018-38.pdf
File-Format: application/pdf
Series: RePEc:ems:eureir
Number: EI2018-38
Classification-JEL: C13, C32
Keywords: BEKK, Rotated BEKK, Diagonal BEKK, Variance targeting, Multivariate GARCH, Consistency, Asymptotic normality
Handle: RePEc:ems:eureir:111553