Semiparametric Maximum Lickelihood Estimation of GARCH Models

We consider a semiparametric GARCH model where the functional form for the conditional density of the errors is unknown. Adaptive conditions of the parameters are examined. Semiparametric Maximum Likelihood (SML) estimators are constructed by maximizing the nonparametric pseudo log-likelihood function computed using the residuals from initial root-n consistent estimates. SML estimators are shown to be adaptive for the adaptively estimable parameters and consistent for all identifiable parameters. Monte Carlo results suggest that SML estimators outperform quasi maximum likelihood estimators and the adaptive maximum likelihood estimators in finite samples.