基于Block Bootstrap的厚尾相依序列下持久性变点检验

Block Bootstrap Tests for Persistence Change in Heavy-Tailed Dependent Sequence

文章讨论了厚尾相依序列下持久性变点检验问题,其中尾指数κ∈(0,2).基于Dickey-Fuller(DF)比值型统计量构造修正的检验统计量,并证明了它在原假设下的渐近分布是一个稳定过程的泛函.在备择假设下,检验统计量具有一致性,且能够正确地识别持久性的变化方向.同时文章还给出了变点位置估计的一致性.而当序列为平稳过程时,所构造的检验统计量也不会产生伪拒绝.由于原假设下统计量的渐近分布包含未知参数κ,因此利用Block Bootstrap抽样方法确定统计量的临界值,从而避免尾指数κ的估计.蒙特卡罗数值模拟结果充分说明了所提出的检验统计量具有鲁棒性.最后通过一组股票数据进一步阐明了文中方法的可行性和有效性.

In this paper,we discuss the problem of persistence change test for heavy-tailed dependent sequences where the tail index.κ∈(0,2)The modified test statistics are constructed based on the Dickey-Fuller(DF)ratio type statistics,and its asymptotic distribution under the null hypothesis is proven to be a functional of a stable process.Under the alternative hypothesis,the test statistics are consistent and can correctly identify the persistence direction of change.At the same time,the consistency of the change point location estimation is also given.When the sequence is a stationary process,the constructed test statistics will not generate spurious rejection.Since the asymptotic distribution of the statistic under the null hypothesis contains the unknown parameterκ,the critical value of the statistic is determined by using the Block Bootstrap sampling method to avoid the estimation of the tail index.The Monte Carlo numerical simulation results fully demonstrate the robustness of the proposed test statistics.Finally,the feasibility and effectiveness of the proposed method are illustrated by a set of stock data.