Georgia Institute of Technology College of Sciences

We analyze a class of semiparametric ARCH models that nests the simple GARCH(1,1) model but has flexible news impact function. A simple estimation method is proposed based on profiled polynomial spline smoothing. Under regular conditions, the proposed estimator of the dynamic coeffcient is shown to be root-n consistent and asymptotically normal. A fast and efficient algorithm based on fast fourier transform (FFT) has been developed to analyze volatility functions with infinitely many lagged variables within seconds. We compare the performance of our method with the commonly used GARCH(1, 1) model, the GJR model and the method in Linton and Mammen (2005) through simulated data and various interesting time series. For the S&P 500 index returns, we find further statistical evidence of the nonlinear and asymmetric news impact functions.