半参数ARCH模型的bootstrap估计

给出了一类半参数自回归条件异方差（ARCH）模型：Yt=m（Yt）＋εt√β0＋β1Yt2其中最εt～iid·N（O，1），m（·）函数的形式不确定，为非参部分；肺，卢。是待估参数，历再万爵为参数部分．结合非参数估计的局部线性拟合方法和参数估计的极大拟似然方法，我们给出估计这类模型的方法．进一步，把该这种方法与bootstrap方法结合起来，同参数方法和半参数方法相比较得出，用半参数的bootstrap方法得出的残差平方和最小，拟合的效果最好．

The Bootstrap Estimation of Seme-parametric ARCH Model

In this paper, we propose a kind of semi-parametric ARCH model： Yt=m（Yt）＋εt√β0＋β1Yt2
where8,iid. N（0, 1 ）, m （ · ） are the nonparametric part with uncertain form of function,/30,~1 are parameters to be estimated, is the parametric part. Combining with local linear fitting method of non-parametric estimation and max-imum likelihood of the parameter estimation, we give the method of estimating such models. Further more, combining this method with bootstrap estimation, we compare the results of the parametric method, semi-parametric method and semi-parametric bootstrap method and find out that the residual sum of squares is minimum and the fitting result is the best by using semi-parametric bootstrap method.