Nonparametric analysis of time series with complex features

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 normal. A simultaneous confidenceband for the nonparametric component is proposed by an efficient one-step spline back-fitting. The performance of our method is evaluated 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.