基于调整样本值域的自正则结构性变化的检验

An Adjusted-range Based on Self-normalized Statistic for Testing Structural Breaks

样本值域被广泛地应用在金融数据波动性分析中,且可以更好地检测高偏度和(或)高峰度的非高斯时间序列的远距离依赖性。本文拓展了Lobato(2001)以及Shao(2010)提出的基于部分和方差的长期方差估计值的自正则统计推断,借鉴Hong和Li(2021)采用部分和调整样本值域的长期方差估计值为自正则因子,设计了一个新的基于调整样本值域的G_(n)^(R)统计量。与Shao和Zhang(2010)提出的G_(n)^(R)统计量类似,基于调整样本值域的G_(n)^(R)统计量也可以应用在期望、相关系数、条件方差等序列的结构性变化检验中,且由于调整样本值域的鲁棒性,其更适用于金融数据分析,具有广泛的应用前景。最后,本文对我国股票市场主要指数的波动性进行了结构性变化检验,并发现波动性的结构性变化普遍存在。

The sample range has been commonly used in modelling volatility of financial data and can detect long-range dependence in non-Gaussian time series with high skewness and/or kurtosis.This paper extends the self-normalization related statistical inference of Lobato(2001)and Shao(2010),which is based on the long run variance estimator of the variance of the partial sum,proposes the use of the adjusted-range of the partial sum as a self-normalizer instead based on Hong and Li(2021),and introduces a new self-normalized adjusted-range based statistic.Similar to the statistic G_(n)^(R)proposed by Shao and Zhang(2010),the G_(n)^(R) statistic based on adjusted-range of the partial sum can be applied to tests for structural breaks in various quantities such as expectation,autocorrelation coefficients,conditional variances,etc.This approach,therefore,has wide applicability and is more suitable to the analysis of financial data.Finally,this paper applies the proposed test statistic for structural breaks in the volatilities in the major Chinese stock indices,finding that structural breaks are common themes in Chinese stock markets.