【作者】 刘君；

【导师】 徐小平； 李拂晓；

【作者基本信息】 西安理工大学 ， 数学， 2021， 硕士

【摘要】 在金融时间序列中,人们常用均值反映资产的平均收益,用方差的变化衡量风险的大小。与单纯的截面数据和时间序列数据相比,面板数据是时间序列和截面数据组成的二维数据集合,能提供更多有用信息。因此,本文基于二元分割法对面板数据中的均值多变点和方差多变点进行了研究,主要研究的内容如下:1.基于拟最大似然法和累积和方法对面板数据模型中方差变点的位置进行了估计,结合二元分割法将上述两种方法推广到方差多变点情形,并证明了变点估计量的相合性。蒙特卡洛模拟讨论了不同的样本量,变点位置和误差项分布对上述两种方法估计效果的影响。模拟结果表明基于拟最大似然型估计量的二元分割法和基于累积和型估计量的二元分割法都能较准确地估计出方差多变点的位置。与基于累积和型估计量的二元分割法相比,基于拟最大似然型估计量的二元分割法的估计效果更优。最后将上述两种方法分别应用于人民币汇率数据和股市周指数数据,结果显示两种方法都能有效估计变点的位置。2.采用基于形态识别的二元分割法分别对面板数据模型中均值多变点和方差多变点的个数和位置进行了估计,证明了变点估计量的相合性。蒙特卡洛模拟主要将基于形态识别的二元分割法与基于全局累积和统计量的二元分割法的估计结果进行比较,分别讨论了不同的样本量和变点位置对两种方法估计效果的影响。模拟结果表明基于形态识别的二元分割法都能较准确地估计出面板数据模型中均值和方差多变点的个数和位置,而且在非线性面板数据模型中也有较好的应用。相比之下,基于全局累积和统计量的二元分割法估计的变点个数一般多于真实变点个数,得到的变点位置与真实变点位置之间的距离也较大。最后将基于形态识别的二元分割法应用于不同的股市周指数数据,说明其有效性。更多还原

【Abstract】 In financial time series,the mean is often used to reflect the average return of assets,and the variance is to measure the risk.Compared with simple cross-sectional data and time series data,panel data is a two-dimensional data collection composed of time series and cross-sectional data,which can provide more useful information.In this paper,multiple change-point estimation in the mean and variance of panel data model is studied based on the binary segmentation method.The main research contents are as follows:1.The change-point estimation in the variance of panel data model based on the quasi-maximum likelihood method and CUSUM method is obtained,and combining with binary segmentation method,the above two methods are extended to multiple change-point estimation in the variance of panel data model,the consistency of change-point estimator is proved.Furthermore,Monte Carlo simulation discussed the influence of different sample size,locations of change-points and error distributions to the estimation results of the above two methods.Monte Carlo experiment shows that the binary segmentation method based on the quasi-maximum likelihood estimator and CUSUM estimator can accurately estimate the location of variance change-point.Compared with the binary segmentation method based on CUSUM estimator,the binary segmentation method based on the quasi-maximum likelihood estimator performs better.Finally,the two methods are applied to the CNY exchange rate data and the stock market weekly index data.The results show that the two methods can effectively estimate the change-points.2.The number and location of multiple change-point in the mean and variance of panel data model is obtained based on the shape-based binary segmentation(Shape-based BS)method,and the consistency of change-point estimator is proved.Monte Carlo simulation compared the estimated resurts of the Shape-based BS method with the BS method which based on global CUSUM statistics,and discussed the influence of different sample size and locations of change-points to the estimation effects of the above two methods respectively.Monte Carlo simulation shows that the Shape-based BS method can accurately estimate the number and location of the change-points,and it also performs better in the nonlinear panel data model.In contrast,the number of change points estimated by the binary segmentation(BS)method which based on global CUSUM statistics is generally more than the number of true change points,and the distance between the estimated change-points and the true change-points is also larger.Finally,the Shape-based BS method is applied to different stock market weekly index data to show its effectiveness.更多还原