异方差非参数回归模型均值与方差变点的小波估计与应用

金融市场中,受突发事件的影响反映资产平均收益的均值函数和反映资产收益波动的方差函数都有可能出现变点. 本文讨论了均值和方差都存在变点的异方差非参数回归模型的变点估计问题. 给出均值函数与方差函数的局部线性估计,利用函数小波系数的特性求得均值与方差变点位置的估计值并给出其收敛速度.在模拟实验中分析变点估计值的样本特性及均值变点估计与方差变点估计的相互影响.最后通过对两组股票数据的均值变点和方差变点进行估计,说明方法的有效性.

Wavelet estimators for change-points in mean and variance of nonparametric regression model and applications

In the practical application, abnormal fluctuations of the mean and variance of model are always possible． In this paper, a method based on wavelet coefficients is proposed to estimate the location of breaks in mean function and variance function of nonparametric regression model. The mean function and variance function can be estimated using local linear fitting. The convergence rate of these estimators are derived. The finite sample properties of the estimators are investigated and the impaction of the changes in mean and variance is analysed by comparing sample deviation, mean square error and standard deviations. Finally, we give practical example to estimate changes in a set of stock price data and HANG SENG INDEX using the wavelet method.