This paper extends kernel weighted GMM estimators recently proposed by the author in the context of homoskedastic processes to a class of models with conditionally heteroskedastic innovations. GMM estimation of such models was previously studied by Kuersteiner (1997, 1999a/b) in the context of ARMA processes and Guo and Phillips (1997) in the context of ARCH processes. Optimal implementation of the GMM estimator requires to include more and more instruments as the sample size grows.
Moment Selection and Bias Reduction for GMM in Conditionally Heteroskedastic ModelsGuido Kuersteiner ,
Econometric Theory and Practice: Frontiers of Analysis and Applied Research, Essays in Honor of Peter C.B. Phillips