基于类方差比统计量的厚尾序列持久性变点研究

发布时间：2018-05-17 07:24

本文选题：持久性变点 + 厚尾指数变点　；参考：《西安科技大学》2017年硕士论文

【摘要】：变点分析作为统计学领域的重要研究课题,一直以来都是国内外学者研究的热点问题。近二十年来越来越多的理论证明,许多经济和金融数据展现持久性特征,且金融数据中出现的“尖峰厚尾”特性能够被厚尾序列更好的刻画。因此,对厚尾序列持久性变点的研究就显得尤为重要。针对厚尾指数较小时,类方差比统计量检验的势函数值偏小的现象,本文在第二章中提出了厚尾序列持久性变点截尾检验方法,通过对原始数据截尾处理,达到提高检验势函数值效果。同时,还得到关于持久性变点位置的一致估计。经过截尾处理之后类方差比统计量是稳健的,即其极限分布是与厚尾指数无关,从而使得在厚尾指数较小的情况下也有良好的检验效果。数值模拟表明,在原假设下,截尾检验并没有明显优势;但在备则假设下能有效的提高检验势函数值。第三章中研究了厚尾指数变点对持久性变点检验的影响。在原假设不存在持久性变点,但含有指数变点的情况下,厚尾指数由大变小即12时,则统计量以2/2-2/1的速度发散,且2-1的值越大发散的速度越快,虽然厚尾指数由小变大时,统计量不再发散到无穷,但数值模拟表明仍存在水平扭曲,只是其水平扭曲没有由大变小时的严重。在备则假设既有持久性变点又有厚尾指数变点时,若12,检验势函数值得到加强,使得更容易拒绝原假设;而k_1≤k_2时,会削弱检验功效。
[Abstract]:As an important research topic in the field of statistics, variable point analysis has always been a hot issue of scholars at home and abroad. In recent twenty years, more and more theories have proved that many economic and financial data show persistent characteristics, and the "peak thick tail" characteristics in financial data can be better depicted by the thick tail sequence. It is very important to study the persistent variation point of the thick tail sequence. In the second chapter, this paper puts forward the method of the truncation test of the persistent variable point of thick tail sequence in the second chapter, to improve the effect of the test potential function. The uniform estimation of the position of the persistent variable points is also obtained. After the truncation, the class variance ratio is robust, that is, its limit distribution is independent of the thick tail exponent, so that it has a good test effect in the case of a small thick tail index. In the third chapter, we study the effect of the thick tail exponential change point on the persistence variable point test in the third chapter. In the case of the original hypothesis, when there is no persistent variable point, but with an exponential change, the thick tail exponent is 12 when the thick tail exponent is smaller, and the higher the value of the 2-1 is diverging. The faster the velocity is, the statistics no longer spread to infinity while the thick tail exponent is larger, but the numerical simulation shows that there is still a horizontal distortion, but the horizontal distortion is not a serious hour. In preparation, if there are both persistent and thick tail exponents, if 12, the test potential function is worth strengthening, making it easier to refuse. The original hypothesis, and k_1 less than k_2, will weaken the efficacy of the test.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212

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