基于Subsampling抽样的厚尾AR(p)序列趋势变点的Ratio检验

Subsampling-based Ratio Test on Trend Change Points in Heavy-tailed

文章考虑的是厚尾AR(p)序列趋势变点检验问题。首先,在已有研究的启发下,构造了一个Ratio统计量来检验趋势变点;其次,在原假设下证明统计量的极限分布是列维过程的泛函,在备择假设下得到统计量的一致性;其次,为了避免参数的估计,采用Subsampling方法获得更为准确的临界值,数值模拟结果显示,在大样本下基于Subsampling抽样方法的Ratio检验很好地控制了经验水平,经验势也达到了比较好的效果;最后,通过一组实证数据进一步阐明理论的有效性和可行性。

This paper considers the trend change point test for heavy-tailed AR(p)sequences.Firstly,inspired by the existing studies,this paper constructs a Ratio statistic to test the trend change point,then proves that the limit distribution of statistics is the functional of Lévy process under the original hypothesis,and obtains the consistency of statistics under the alternative hypothesis.Finally,in order to avoid parameter estimation,the paper uses Subsampling method to obtain more accurate critical values.The numerical simulation results show that the Ratio test based on Subsampling method can well control the experience level and the experience potential in a large sample.In addition,a group of empirical data is used to further clarify the validity and feasibility of the theory.