长记忆序列两类变点问题的研究

发布时间：2018-02-28 12:25

本文关键词： 长记忆序列结构变点伪回归非参数模型　出处：《西安科技大学》2016年硕士论文　论文类型：学位论文

【摘要】：变点问题在统计学领域一直是国内外学者的研究热点问题之一。随着经济迅速发展以及不断的多样化,在金融时间序列中存在结构变点愈加频繁;与此同时,越来越多的金融数据会呈现长期记忆特性,不能用常见的正态分布来描述。鉴于此,对长记忆序列变点问题的研究更显的十分重要。本文主要是在现有变点问题研究方法的基础上将变点与长记忆序列相结合作了较为系统的研究。第一类长记忆变点问题,建立了两种含结构变点的长记忆序列模型,基于t-检验统计量研究序列的伪回归现象。研究结果表明:t-检验统计量是以1/2的速度发散的,因此产生伪回归。通过蒙特卡罗数值模拟,对伪回归现象的影响因素作了灵敏度分析,以此来验证统计量的渐近分布的正确性。结果表明:两列长记忆序列只要都存在结构变点,无论变点时刻是否相同,t-检验统计量拒绝率都会随着样本量的增大而增大,从而产生伪回归现象;伪回归现象不仅跟长记忆序列的变点时刻和样本量大小有关,而且对长记忆指数也是非常的敏感;含趋势变点的长记忆序列比含均值变点的长记忆序列更容易产生伪回归现象。第二类长记忆变点问题,分别考虑了非参数回归模型中噪声的长记忆指数变点以及回归函数变点问题。回归函数结构变点部分,给出了基于回归函数局部线性核估计的检验统计量以及变点时刻分位数的估计量,推导得到统计量在原假设和备择假设下的渐近分布,并证明了检验和估计的一致性。通过蒙特卡罗数值模拟,采用Bootstrap检验方法给出在备择假设下的经验势函数值以及变点位置的估计值。长记忆指数变点部分,基于残差序列的平方构造CUSUM检验统计量并推导其渐近分布,并在一定条件下证明了原假设下检验统计量收敛于Brown桥的上确界。同样通过数值模拟给出在备择假设下的经验势函数值和变点位置估计值。数值模拟结果表明:本文给出的方法对回归函数变点以及长记忆指数变点的检测和估计都有良好的功效。
[Abstract]:The change point problem has always been one of the hot topics in the field of statistics. With the rapid development and diversification of economy, structural change points in the financial time series become more and more frequent. More and more financial data exhibit long-term memory characteristics that cannot be described by the usual normal distribution. It is more important to study the change point problem of long memory sequence. In this paper, based on the existing research methods of change point problem, we combine the change point problem with the long memory sequence to make a more systematic study. The first kind of long memory change point problem is the long memory change point problem, the first kind is the long memory change point problem. In this paper, two kinds of long memory sequence models with structural change points are established, and the pseudo regression phenomena of the series are studied based on the t- test statistics. The results show that the 10% t- test statistics diverge at a speed of 1/2. Therefore, pseudo regression is produced. By Monte Carlo numerical simulation, sensitivity analysis of the influencing factors of pseudo regression phenomenon is made. The results show that as long as there are structural change points in two long memory sequences, the rejection rate of the statistics will increase with the increase of sample size, regardless of whether the change point is the same or not at the same time. The phenomenon of pseudo regression is not only related to the change point time and sample size of long memory sequence, but also sensitive to long memory index. Long memory sequences with trend change points are more likely to produce pseudo regression than long memory sequences with mean change points. In this paper, we consider the long memory exponential change point of noise and the change point problem of regression function in nonparametric regression model. The test statistics based on the local linear kernel estimator of regression function and the estimator of the quantile at the change point are given. The asymptotic distributions of the statistics under the original and alternative assumptions are derived. The consistency of test and estimation is proved. By Monte Carlo numerical simulation, the empirical potential function value under alternative hypothesis and the estimated value of change-point position are given by using Bootstrap test method. The CUSUM test statistics are constructed based on the squared residuals and their asymptotic distributions are derived. Under certain conditions, it is proved that the test statistics converge to the upper bound of the Brown bridge under the original hypothesis. The empirical potential function values and the change point position estimates under alternative assumptions are also given by numerical simulation. The numerical simulation results show that:. The method presented in this paper has a good effect on the detection and estimation of the change points of regression function and the long memory index.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

【相似文献】