【作者】 张华高；

【导师】 郑明； 金曙松；

【作者基本信息】 复旦大学 ， 统计学， 2010， 硕士

【摘要】 本文提出了一套用来对金融时间序列的波动率进行预测的且有着较强适应性的非参数GARCH-M建模方法。基于模拟数据和实际数据对非参数GARCH-M模型和简单参数GARCH-M模型的估计和预测效果比较发现,本文提出的非参数GARCH-M模型在对波动率的估计和预测效果上都显著的优于参数GARCH-M模型。本文构造的非参数GARCH-M模型是基于前期收益率序列和前期波动率估计序列的双变量B样条基回归方法得出的。在模拟研究中发现,协分梯度下降算法得出的优化模型的拟合效果严重地依赖于迭代次数M的选择。本文基于检验样本的模型拟合信息准则Hanna-Quinn的值最小化来选择迭代次数M,通过对模拟数据的研究发现此方法能有效地防止波动率估计出现异常值。在对模型优化的算法上,本文在更新波动率估计的同时也更新了模型均值方程系数的估计,并在模拟研究中发现这能显著地提高对均值方程系数估计的准确度。最后基于美国纳斯达克银行指数的实证分析结果表明在对波动率的预测的效果上,本文提出的B样条GARCH-M模型显著的优于参数GARCH-M模型。更多还原

【Abstract】 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.更多还原