分段平稳时间序列中的多变点检测
Multiple Change-Points Detection of Piecewise Stationary Time Series
DOI: 10.12677/PM.2018.82018, PDF,  被引量    国家自然科学基金支持
作者: 吴 楠*, 王 丹：贵州大学数学与统计学院，贵州 贵阳；胡 尧：贵州大学数学与统计学院，贵州 贵阳；贵州省公共大数据重点实验室，贵州 贵阳
关键词: 多变点；似然比；置信区间；最小描述长度准则；Multiple Change-Points； Likelihood Ratio； Confidence Intervals； Minimum Description Length Criterion
摘要: 变点问题在工业、金融、气象等领域有着广泛的应用。针对分段平稳时间序列的多变点检测，提出一种通过构建似然比扫描(LRS)统计量，结合最小描述长度(MDL)准则对变点数量、位置进行估计的方法，将计算上不可行的全局多变点估计问题通过有效分段降为各局部窗口中的多个单变点检测问题。同时对每个估计变点构建了置信区间，为描述变点提供更多信息。最后通过大量数值模拟和交通实例分析证明方法的有效性。
Abstract: The change-point problem has a wide range of applications in the industrial, financial, meteorology and other fields. A method for estimating the numbers, locations of change-point by building the Likelihood ratio scan (LRS) statistics, combined with the Minimum description length (MDL) principle has been proposed. It reduces the computationally infeasible global mul-tiple-change-point estimation problem to a number of single-change-point detection problems in various local windows by effective segmentation. In order to provide more information for describing change points, we have constructed confidence intervals for each of the change points. Finally, extensive simulation studies and example analysis of traffic show the LRS usability practice.
文章引用：吴楠, 胡尧, 王丹. 分段平稳时间序列中的多变点检测[J]. 理论数学, 2018, 8(2): 136-148. https://doi.org/10.12677/PM.2018.82018

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