一种基于秩的高维时间序列ARCH效应和序列相关性检验方法  

A Rank Based Method for Testing ARCH Effect and Serial Correlation of High-dimensional Time Series

作　　者：周泽人 ZHOU ZEREN(School of Statistics,Capital University of Economics and Business,Beijing 100070,China)

机构地区：[1]首都经济贸易大学统计学院,北京100070

出　　处：《应用数学学报》2025年第1期69-88,共20页Acta Mathematicae Applicatae Sinica

基　　金：首都经济贸易大学校级青年学术创新团队建设项目(QNTD202303)资助项目。

摘　　要：本文提出了一种基于L_(2)范数和Spearman相关性系数的检验高维时间序列的序列相关性和自回归条件异方差效应的假设检验方法.本文研究了所提的统计量的渐近性质,并提出了一种基于自助法的计算临界值的方法,证明了所提假设检验方法可以控制第一类错误的概率.我们的假设检验方法是维数自由的,即对数据的维数没有要求,从而可以用于高维时间序列的情况,同时本方法对数据的尾部性质没有要求,从而可以用于重尾的情况.我们使用了数值模拟和实际数据来说明本文所提方法的有效性.This article proposes a hypothesis testing method to detect serial correlation and ARCH effect in high-dimensional time series based on L_(2) norm and Spearman's correlation.In this article,We study the asymptotic behavior of our test statistic and provide a bootstrap-based approach to generate critical values,we prove our test can control Type-Ⅰ errors.Our test is dimensional-free,which means it is independent of the dimension of the data,hence our test can be used for high dimensional time series data.Our test does not require tail properties of data,hence it can be used for heavy-tailed time series.The simulation results indicate that our new test performs well in both empirical sizes and powers and outperforms other tests.The practical usefulness of our test is illustrated via simulation and a real data analysis.

关 键 词：ARCH效应 高维时间序列 秩统计量 序列相关性 

分 类 号：O212.1[理学—概率论与数理统计]