基于M估计强混合重尾序列结构变点的鲁棒检验

Robustness Test of M-Estimation-based Change Points of Strongly Mixed Heavy Tail Sequence Structures

针对强混合重尾序列结构变点的检测问题,为避免因序列重尾性导致最小二乘估计产生偏差,文章提出了基于M估计的比值型检验统计量,用于检测重尾序列位置结构变点。在一般约束条件下证明了原假设下统计量的极限分布是布朗运动的泛函,并得到备择假设下的一致性。针对因序列相依性导致的经验水平扭曲现象,采用Block Bootstrap抽样方法获得了更为准确的临界值,有效提高了检验功效。数值模拟结果显示,在Block Bootstrap抽样方法下基于M估计的比值型检验在强混合重尾序列结构变点检测中能较好地控制经验水平,经验势也较合理。最后,通过一组汇率数据验证了所提检验方法的可行性。

In view of the detection of change points of strongly mixed heavy tail sequence structures,and in order to avoid the ordinary least square deviation caused by a heavy-tailed sequence,this paper proposes an M-estimate-based ratio-type statistic to test the change point with a heavy-tailed sequence.Under general constraints,it is proved that the limit distribution of the sta-tistics under the null hypothesis is the functionality of Brownian motion,and the consistency under the alternative hypothesis is ob-tained.Aiming at the experience level distortion caused by sequence dependence,the Block Bootstrap sampling method is used to obtain a more accurate critical value,which effectively improves the inspection efficiency.The numerical simulation results show that the M-estimation-based ratio-type test under the Block Bootstrap sampling method can better control the experience level and reasonable experience potential in the change point detection of strongly mixed heavy-tailed sequence structure.Finally,the feasibility of the proposed test method is verified by a set of exchange rate data.