Efficient Semiparametric GARCH Modeling of Financial Volatility

• Activity Number: 623
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Li Wang and Qiongxia Song*+ and Lijian Yang
• Companies: University of Georgia and The University of Texas at Dallas and Michigan State University
• Keywords: B-spline ; confidence band ; knots ; news impact curve ; 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 normal. A simultaneous confidence band for the nonparametric component is proposed by an efficient one-step spline backfitting. 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.