Feasible generalized least squares estimation of multivariate GARCH(1,1) models
A feasible generalized least squares estimator for multivariate GARCH(1,1) models is suggested and its theoretical properties are investigated. Under mild assumptions the estimator is consistent and asymptotically normal distributed with the same variance as the quasi-maximum likelihood estimator. As a drawback the corresponding estimator can result in non-stationary models or conditional volatility matrices that are not positive semidefinite. The estimator relies on a consistent inital estimator such as the closed-form estimator by the authors [ibid. 120, 152--162 (2013; Zbl 1282.62202)], which is also used as a starting value in the accompanying simulation study. In these simulations, the mean squared error of the proposed procedure improves this closed-form estimator by a great deal but is usually somewhat outperformed by the quasi-maximum-likelihood estimator (where in some scenarios it can even achieve comparable results). On the plus side the proposed estimator is considerably faster than the quasi-maximum-likelihood estimator as it does not rely on advanced optimization techniques.
scientific article; zbMATH DE number 6305107
scientific article