非参数趋势项时间序列自协方差函数的变点检测  

TESTING FOR AUTOCOVARIANCES CHANGES IN TIME SERIES MODELS WITH NONPARAMETRIC TRENDS

作　　者：张瑞红[1] 王立洪[1] 

机构地区：[1]南京大学数学系,南京210093

出　　处：《南京大学学报（数学半年刊）》2017年第1期76-96,共21页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：国家自然科学基金资助项目(No.11671194;11171147;11501287)

摘　　要：本文主要考虑带有非参数趋势项时间序列的自协方差函数的变点检测问题.本文采用局部多项式对趋势项进行拟合,并对去除趋势项后的时间序列,通过累积和(CUSUM)统计量进行变点分析.在GMC条件及一些正则性假设下,我们讨论了检验统计量在原假设和备择假设下的渐近性质及检验的相合性.实证方面,我们运用0-5阶的局部多项式分别对带有AR(1)误差的模型进行估计,并进行变点检测.通过检验水平和经验功效的比较分析,验证了有限样本下检验方法的有效性.In this paper, we consider the change-point detection in autocovariances of time series with nonparametric trends. We first fit the trend by local polynomial estimation, and then detect changes after detrending using the cumulative sum （CUSUM） statistic. Under the GMC condition and some regularity assumptions, we investigate the asymptotic properties of the test statistic and the consistency of the test. In simulation studies, we use local polynomials of order 0-5 to fit the trend of the time series model with AR（1） error, and carry out simulations to detect change-point in autocovariances of the error. By comparing the empirical size and empirical power, we show the good performance of the test under finite sample.

关 键 词：自协方差 变点检测 相合性 累积和统计量 局部多项式估计 

分 类 号：O211.61[理学—概率论与数理统计]