标题： 检验非参数自回归中创新分布的变化——基于序列经验过程的方法 显示英文标题

标题： Testing for a change of the innovation distribution in nonparametric autoregression - the sequential empirical process approach

摘要： 我们研究了一个在条件异方差性下的非参数自回归模型，目的是检验创新分布是否随时间变化。 为此，我们为非参数估计的创新（残差）的序列经验过程开发了渐近展开式。 我们建议基于从最初的ns个和最后的n-ns个残差构建的估计创新分布之间的差异来构造一个基于Kolmogorov-Smirnov统计量。 在没有变点的零假设下，证明了基础随机过程弱收敛于高斯过程。 该结果表明，该检验在渐近意义上是分布自由的。 证明了检验对于固定备择假设的一致性。 通过模拟研究调查了所提出检验的小样本性能，并将其应用于数据实例。 显示英文摘要

摘要： We consider a nonparametric autoregression model under conditional heteroscedasticity with the aim to test whether the innovation distribution changes in time. To this end we develop an asymptotic expansion for the sequential empirical process of nonparametrically estimated innovations (residuals). We suggest a Kolmogorov-Smirnov statistic based on the difference of the estimated innovation distributions built from the first ns and the last n-ns residuals, respectively. Weak convergence of the underlying stochastic process to a Gaussian process is proved under the null hypothesis of no change point. The result implies that the test is asymptotically distribution-free. Consistency against fixed alternatives is shown. The small sample performances of the proposed test is investigated in a simulation study and the test is applied to data examples.