Two-stage weighted least squares estimator of multivariate conditional mean observation-driven time series models

We introduce a general parametric multivariate model where the first two conditional moments are assumed to be multivariate time series. The focus of the estimation is the conditional mean parameter vector. Quasi-Maximum Likelihood Estimators (QMLEs) based on the linear exponential family are typically employed for such estimation problems when the true multivariate conditional probability distribution is unknown or too complex. Although QMLEs provide consistent estimates they may be inefficient. In this paper we study a two-stage Multivariate Weighted Least Square Estimators (MWLSEs), which enjoy the same consistency property as the QMLEs and provides efficiency gain with suitable choice of the covariance matrix. We compare the estimation performance of the QMLEs and MWLSEs through simulation experiments.