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Statistica Sinica 22 (2012), 249-270




Li Wang$^{1}$, Cong Feng$^{1}$, Qiongxia Song$^{2}$ and Lijian Yang$^{3,4}$

$^{1}$University of Georgia, $^{2}$University of Texas at Dallas,
$^{3}$Soochow University and $^{4}$Michigan State University

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.

Key words and phrases: B-spline, confidence band, knots, news impact curve, volatility.

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