Efficient Semi-Parametric Estimation of Non-Gaussian GARCH Processes

Semi-parametric estimators for non-Gaussian GARCH processes based on Feasible Weighted Least Squares (FWLS) are proposed. The estimators are consistent and do not require the specification of the innovations distribution family. The FWLS estimators incorporate information related to the skewness and kurtosis of residuals. This improves their efficiency in comparison to Normal Quasi-Maximum Likelihood (NQML) estimators which only rely on the first two conditional moments. The improved efficiency of FWLS estimators is illustrated in a simulation experiment; the estimation RMSE decreases observed by using the FWLS estimator instead of the NQML range between 0.07% and 10.3% for all parameters of the considered NGARCH with Variance-Gamma innovations. The methodology is also shown to be applicable for the estimation of multivariate GARCH processes