中文摘要：

本文讨论了非参数自回归模型异方差的检验问题。在非参数自回归模型的建模过程中,通常假定方差为常数。然而在建模前,我们应该首先检验这一假定是否成立。本文将利用小波方法来检验异方差问题。我们首先利用核估计方法定义经验小波系数,然后讨论其渐近性质。在此基础上,我们提出了异方差性检验的统计量。数值模拟结果表明,我们的方法表现良好。

英文摘要：

A wavelet-based test for heteroscedasticity in a nonparametric autoregressive model is considered.In modelling a nonparametric autoregressive model,homoscedasticity is usually assumed.However,we should test if this assumption is true before modelling. The wavelet based method is used to test heteroscedasticity in this paper.The empirical wavelet coefficients are given by the kernel method and shown to be asymptotically i.i.d. normal,based on which,the test statistic for heteroscedasticity is constructed.Simulation study shows that our method performs well.