长记忆时间序列的均值单变点估计  

Mean Univariate Point Estimation of Long Memory Time Series

作　　者：习代青 肖洪策 Xi Daiqing;Xiao Hongce(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073

出　　处：《统计与决策》2024年第3期51-57,共7页Statistics & Decision

基　　金：中央高校基本科研业务费专项资金资助项目(2722021BZ035)。

摘　　要：文章采用拟极大似然法估计了一类长记忆时间序列模型的单均值变点,在变点大小固定和变点收缩两种情形下分析了估计量的渐近性质。研究发现,变点大小与长记忆性之间存在一种权衡关系。具体而言,当变点大小固定时,变点估计量是不相合的,而变分点估计量是T-相合的;当变点收缩时,变点估计量的收敛速度依赖于记忆参数d,估计量的极限分布得以推导。最后,蒙特卡洛实验和实证分析验证了所提理论结果的有限样本表现。This paper uses the quasi-maximum likelihood method to estimate the change point in means of long memory time series model,and analyzes the asymptotic properties of the estimator under both the cases of fixed break magnitude and shrinking break magnitude.The research finds that there is a trade-off between the break magnitude and long memory dependency.Concretely speaking,in the case of fixed break magnitude,there exists inconsistency of the estimator for the break location,but the T-consistency of the estimator for the break fraction;in the case of shrinking break magnitude,the convergence rate of the estimator hinges on the memory parameter d,with the limit distribution of the estimator derived.Finally,Monte Carlo experiment and an empirical analysis are conducted to verify the limited sample performance of the proposed theoretical results.

关 键 词：长记忆 分数布朗运动 结构变点 拟极大似然估计 最小二乘法 

分 类 号：O212.1[理学—概率论与数理统计]