回归模型参数的变点检测方法研究

摘要/Abstract

摘要：

该文基于非平稳性度量指标（NS）构造了检测回归模型参数变点的方法.在选择合适的参数估计方法和窗口大小的前提下，计算窗口内样本的残差序列及对应的NS值，通过判断窗口内残差序列的平稳性从而达到变点检测的目的.构造一系列二分段回归模型进行实验验证，结果表明该方法能够有效检测到二分段回归模型的变点位置，与其它方法的对比实验结果也表明了该方法在回归模型参数变点的检测中准确性更高.

关键词: 回归模型, 变点检测, 非平稳性度量

Abstract:

This paper constructs a method to detect the change point of regression model parameters based on the non-stationary measurement index (NS). Under the premise of selecting the appropriate parameter estimation method and window size, the residual sequence of the sample in the window and the corresponding NS value are calculated by judging the stationarity of the residual sequence within the window to achieve the purpose of change point detection. A series of two-segment regression models are constructed for experimental verification. The results show that this method can effectively detect the position of the change point of the two-segment regression model. The experimental results of comparison with other methods also show that the method is more accurate in the detection of regression model parameter change points.

Key words: Regression model, Change point detection, Non-stationary measure

中图分类号:

O212

郑金辉,余旌胡,丁义明,鲍泽宇. 回归模型参数的变点检测方法研究[J]. 数学物理学报, 2021, 41(4): 1124-1134.

Jinhui Zheng,Jinghu Yu,Yiming Ding,Zeyu Bao. Research on Change-Point Detection for Parameters in Regression Model[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1124-1134.

图/表 11

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图 (5c)

表 2

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变点位置$l_{1}+1$	无变点	11	41	101	161	191
模型四	100	94.5	98.5	96.5	98.5	99
模型五	100	95	94.5	95.5	99.5	99
模型六	100	94.5	97.5	98	97	98.5

方法	LAD			NS
变点位置	31	81	181	31	81	181
一元线性	79.256	77.196	77.890	1.178	0.702	0.970
多元线性	74.172	76.543	74.306	0.684	0.489	1.015
非线性	133.999	111.789	141.534	23.933	16.690	19.350

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