Efficient semiparametric garch modeling of financial volatility

Abstract

We consider a class of semiparametric GARCH models with additive autoregressive components linked together by a dynamic coefficient. We propose estimators for the additive components and the dynamic coefficient based on spline smoothing. The estimation procedure involves only a small number of least squares operations, thus it is computationally efficient. Under regularity conditions, the proposed estimator of the parameter is root-n consistent and asymptotically nor- mal. A simultaneous confidence band for the nonparametric component is proposed by an efficient one-step spline backfitting. The performance of our method is evalu- ated by various simulated processes and a financial return series. For the empirical financial return series, we find further statistical evidence of the asymmetric news impact function.