Improved Estimation of Dynamic Models of Conditional Means and Variances

Modelling dynamic conditional heteroscedasticity is the daily routine in time series econometrics. We propose a weighted conditional moment estimation to potentially improve the efficiency of the QMLE (quasi maximum likelihood estimation). The weights of conditional moments are selected based on the analytical form of optimal instruments, and we nominally decide the optimal instrument based on the third and fourth moments of the underlying error term. This approach is motivated by the idea of general estimation equations (GEE). We also provide an analysis of the efficiency of QMLE for the location and variance parameters. Simulations are conducted to show the better performance of our estimators