基于积分方差一致估计的非参数跳检验方法  

Nonparametric Jump Test Method Based on Consistent Estimation of Integral Variance

作　　者：李亚爽 赵春明 冯雪峰 Li Yashuang;Zhao Chunming;Feng Xuefieng(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,成都611756

出　　处：《统计与决策》2022年第15期10-15,共6页Statistics & Decision

基　　金：教育部人文社会科学研究规划基金项目(20XJAZH009);西南交通大学新时代“大思政”育人工作项目(DSZ2019-ZLTS-19);西南交通大学研究生研究类教育改革项目(YJG4-2020-Y035)。

摘　　要：文章针对二次幂变差在有限样本情形下低估跳跃性波动的问题,首先,提出了一种估计积分方差的修正已实现二次幂极差(CRBV)方法;然后,基于LM检验原理分别构造了跳检验统计量J_CRBV和J_CTBPV,并给出二阶矩过程依概率收敛的定理,证明了当积分方差由其一致估计量替换时所构造的检验统计量仍服从标准正态分布;最后,用蒙特卡洛模拟表明两种跳检验统计量均有效可行,并将其应用到沪深300股指期货市场,结果表明股指期货资产价格存在周末效应和周内效应。Dealing with the problem of underestimating the jump fluctuation of quadratic variation in the case of finite samples, this paper firstly proposes a Corrected Realized Range-based Bi-power Variation(CRBV) method for estimating integral variance, and then constructs jump test statistics J_CRBV and J_CTBPV separately based on LM test principle, presenting the theorem that the second-order moment process converges in probability, and proving that when the integral variance is replaced by its consistent estimator, the constructed test statistics still obey the standard normal distribution. Finally, Monte Carlo simulation is done to show that the two jump test statistics are both effective and feasible, that when the two are applied to CSI 300 stock index futures market, the results show that there are weekend effect and weekday effect in stock index futures asset price.

关 键 词：高频数据 积分方差 跳跃 周内效应 周末效应 

分 类 号：O212.1[理学—概率论与数理统计]