Asymptotic and Finite Sample Properties for Multivariate Rotated GARCH Models

This paper derives the statistical properties of a two-step approach to estimating multivariate rotated GARCH-BEKK (RBEKK) models. From definition RBEKK, unconditional covariance matrix is estimated in first step rotate observed variables order have identity for its sample matrix. In second step, remaining parameters are by maximizing quasi-log-likelihood function. For this quasi-maximum likelihood (2sQML) estimator, shows consistency and asymptotic normality under weak conditions. While second-order moments needed matrix, existence finite sixth-order required convergence derivatives also relationship between distributions 2sQML estimator RBEKK model variance targeting VT-BEKK model. Monte Carlo experiments show that bias negligible appropriateness diagonal specification depends on closeness either BEKK or An empirical analysis returns stocks listed Dow Jones Industrial Average indicates choice models changes over time, but most differences two forecasts negligible.