基于Bootstrap方法的厚尾AR(p)序列均值变点检验

Bootstrap Procedures for Mean Change Point Detection in AR(p) Heavy-Tailed Series

讨论了新息过程为p阶厚尾自回归过程的均值变点检验问题.基于修正的Ratio检验统计量,在原假设下证明了统计量的极限分布是Lévy过程的泛函,并得到在备择假设下的一致性.为了避免对未知参数的估计,采用Bootstrap子抽样方法以得到更精确的统计量临界值.蒙特卡洛模拟表明,基于Bootstrap方法的Ratio检验统计量不仅很好地控制了经验水平,且经验势也达到令人满意的效果.

The problem of mean changes test when the innovation process is a p-order heavy-tailed autoregressive process is examined.On the basis of the modified ratio statistic,we prove that the limiting distribution of the ratio statistic is a functional of Lévy process under the original hypothesis,and the consistency is obtained under the alternative hypothesis.To avoid estimation of the unknown parameters,we adopt a bootstrap method to return more accurate critical values.Monte Carlo simulation shows that the bootstrap-based ratio test statistic not only well controls the empirical sizes,but also achieves the satisfactory empirical powers.