Nonparametric GARCH-M Model For Financial Volatility

We propose a flexible generalized auto-regressive conditional heteroscedasticity in mean type of model for the estimates and forecasts of volatility in financial time series in this paper. The approach based on nonparametric GARCH-M model significantly outperforms the classical GARCH-M model in the prediction of financial volatility, in term of the comparison in the estimates and forecasts of the volatility of simulated and real data by the parametric GARCH-M and nonparametric GARCH-M. The nonparametric GARCH-M model proposed in this paper is based on the idea of using bivariate B-splines of lagged rates of return and estimated volatilities. We found in the simulated data analysis that the effect of co-ordinatewise gradient descent algorithm on the prediction of the volatility significantly depends on the choice of the iteration times-M. The optimal choice of M in this paper is the value that minimizes the modeling information criteria-Hanna-Quinn of validate sample, and the simulated data analysis results shows that the method can effectively avoid outliers in the estimates of the volatilities. As to the algorithm for model optimizing, we update the coefficients'estimates of mean equation as well as the estimates of volatilities, and it is showed in the simulation study that the method can improve the accuracy of the coefficients'estimates of mean equation significantly. Also, we apply the approach to American NASDAQ Bank Index analysis, and we found that the B-splines GARCH-M model outperforms the parametric GARCH-M model in the prediction of volatility of NASDAQ Bank Index significantly.