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

图 1

图 2

图 3

表 1.1

一元线性模型不同变点位置的检验能力"

变点位置 $l_{1}+1$	无变点	11	41	101	161	191
模型一	100	95.5	96	98	99	99
模型二	100	96.5	97	99	98	99
模型三	100	95.5	97	97.5	97.5	99

表 1.1

表 1.2

多元线性模型不同变点位置的检验能力"

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

表 1.2

表 1.3

非线性模型不同变点位置的检验能力"

变点位置 $l_{1}+1$	无变点	11	41	101	161	191
模型七	100	90	93	95.5	96	95.5
模型八	100	96	92	94	96.5	96.5
模型九	100	92.5	94	92	95.5	98

表 1.3

图 4

图 (5a)

图 (5b)

图 (5c)

表 2

参考文献 27

1	Page E S . Continuous inspection schemes. Biometrika, 1954, 41 (1/2): 100- 115 doi: 10.2307/2333009
2	Inclán C , Tiao G C . Use of cumulative sums of squares for retrospective detection of changes of variance. Journal of the American Statistical Association, 1994, 89 (427): 913- 923
3	Goossens C , Berger A . Annual and seasonal climatic variations over the northern hemisphere and Europe during the last century. Annales Geophysicae, 1986, 4 (4): 385- 400
4	Pettitt A N . A nonparametric approach to the change-point problem. Journal of the Royal Statistical Society: Series C (Applied Statistics), 1979, 28 (2): 126- 135
5	谭常春, 陈思, 缪柏其. 跳-斜度变点估计的强收敛速度. 中国科学技术大学学报, 2011, 41 (9): 773- 777 doi: 10.3969/j.issn.0253-2778.2011.09.004
	Tan C C , Chen S , Miao B Q . The strong convergence rate of jump-slope change point estimation. Journal of University of Science and Technology of China, 2011, 41 (9): 773- 777 doi: 10.3969/j.issn.0253-2778.2011.09.004
6	谭智平, 缪柏其. 关于分布变点问题的非参数统计推断. 中国科学技术大学学报, 2000, 3, 21- 28
	Tan Z P , Miao B Q . Nonparametric statistical inference on the distribution change point. Journal of University of Science and Technology of China, 2000, 3, 21- 28
7	Oh H , Lee S . On score vector-and residual-based CUSUM tests in ARMA-GARCH models. Statistical Methods & Applications, 2018, 27 (3): 385- 406
8	叶五一, 缪柏其, 谭常春. 基于分位点回归模型变点检测的金融传染分析. 数量经济技术经济研究, 2007, 24 (10): 151- 160 doi: 10.3969/j.issn.1000-3894.2007.10.015
	Ye W Y , Miao B Q , Tan C C . Analysis of financial contagion based on change point detection of quantile regression model. Quantitative and Technical Economic Research, 2007, 24 (10): 151- 160 doi: 10.3969/j.issn.1000-3894.2007.10.015
9	叶五一, 缪柏其. 基于Copula变点检测的美国次级债金融危机传染分析. 中国管理科学, 2009, 17 (3): 1- 7 doi: 10.3321/j.issn:1003-207X.2009.03.001
	Ye W Y , Miao B Q . Analysis of the contagion of U.S. subprime debt financial crisis based on copula change coint detection. Chinese Management Science, 2009, 17 (3): 1- 7 doi: 10.3321/j.issn:1003-207X.2009.03.001
10	Lattanzi C , Leonelli M . A change point approach for the identification of financial extreme regimes. Statistics, 2019, 19 (1): 1- 34
11	Perreault L , Bernier J , Bobée B , et al. Bayesian change-point analysis in hydrometeorological time series. Part 1:The normal model revisited. Journal of Hydrology, 2000, 235 (3-4): 221- 241 doi: 10.1016/S0022-1694(00)00270-5
12	Chen S , Li Y , Kim J , et al. Bayesian change point analysis for extreme daily precipitation. International Journal of Climatology, 2017, 37 (7): 3123- 3137 doi: 10.1002/joc.4904
13	Hu J . Cancer outlier detection based on likelihood ratio test. Bioinformatics, 2008, 24 (19): 2193- 2199 doi: 10.1093/bioinformatics/btn372
14	Wu D , Faria A V , Younes L , et al. Mapping the order and pattern of brain structural MRI changes using change-point analysis in premanifest Huntington's disease. Human Brain Mapping, 2017, 38 (10): 5035- 5050 doi: 10.1002/hbm.23713
15	Quandt , Richard E . The estimation of the parameters of a linear regression system obeying two separate regimes. Journal of the American Statistical Association, 1958, 53 (284): 873- 880 doi: 10.1080/01621459.1958.10501484
16	Quandt , Richard E . Tests of the hypothesis that a linear regression system obeys two separate regimes. Journal of the American Statistical Association, 1960, 55 (290): 324- 330 doi: 10.1080/01621459.1960.10482067
17	Liu Zhihua , Qian Lianfen . Changepoint estimation in a segmented linear regression via empirical likelihood. Communications in Statistics-Simulation and Computation, 2010, 39 (1): 85- 100
18	Lee S , Seo M H , Shin Y . Testing for threshold effects in regression models. Journal of the American Statistical Association, 2011, 106 (493): 220- 231 doi: 10.1198/jasa.2011.tm09800
19	Bai J . Estimation of a change point in multiple regression models. Review of Economics and Statistics, 1997, 79 (4): 551- 563 doi: 10.1162/003465397557132
20	蒋家坤, 林华珍, 蒋靓, 等. 门槛回归模型中门槛值和回归参数的估计. 中国科学: 数学, 2016, 46 (4): 41- 54
	Jiang J K , Lin H Z , Jiang L , et al. Estimation of threshold and regression parameters in threshold regression model. Science in China: Mathematics, 2016, 46 (4): 41- 54
21	Tang Y C , Wang P P , Chen H . Bayesian analysis for change-point linear regression models. Chinese Journal of Applied Probability and Statistics, 2015, 31 (1): 89- 102
22	Ciuperca G . The M-estimation in a multi-phase random nonlinear model. Stats & Probability Letters, 2009, 79 (5): 573- 580
23	Ciuperca G . Estimating nonlinear regression with and without change-points by the LAD method. Annals of the Institute of Statal Mathematics, 2011, 63 (4): 717- 743
24	Boldea O , Hall A R . Estimation and inference in unstable nonlinear least squares models. Journal of Econometrics, 2013, 172 (1): 158- 167
25	谭秋衡. 时间序列的非平稳性度量及其应用[D]. 北京: 中国科学院研究生院, 2013
	Tan Q H. Non-Stationary Measurement of Time Series and Its Application[D]. Beijing: Graduate School of Chinese Academy of Sciences, 2013
26	谭秋衡, 丁义明. 基于非平稳性度量的彩票数据实证分析. 数学物理学报, 2014, 34 (1): 207- 216
	Tan Q H , Ding Y M . Empirical analysis of lottery data based on non-stationarity measure. Acta Math Sci, 2014, 34 (1): 207- 216
27	谭秋衡, 吴量, 李波. 基于EMD及非平稳性度量的趋势噪声分解方法. 数学物理学报, 2016, 36 (4): 783- 794
	Tan Q H , Wu L , Li B . Decomposition of noise and trend based on EMD and non-stationarity measure. Acta Math Sci, 2016, 36 (4): 783- 794

Metrics

Viewed

Full text

145

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	3	0	0	142

	From	local

	Times	145
	Rate	100%

Abstract

113

Just accepted	Online first	Issue

0	0	113

From	Others	local

Times	112	1
Rate	99%	1%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

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

[1]	王志刚,丁义明. 信噪比在AR模型定阶方法选择中的研究[J]. 数学物理学报, 2020, 40(3): 811-823.
[2]	谭秋衡, 吴量, 李波. 基于EMD及非平稳性度量的趋势噪声分解方法[J]. 数学物理学报, 2016, 36(4): 783-794.
[3]	谭秋衡, 丁义明. 基于非平稳性度量的彩票数据实证分析[J]. 数学物理学报, 2014, 34(1): 207-216.
[4]	王成勇. 半参数平滑转换回归模型及其级数估计[J]. 数学物理学报, 2012, 32(4): 797-807.
[5]	丁义明, 范文涛, 谭秋衡, 吴克坤, 邹永杰. 数据流的非平稳性度量——纪念李国平院士吴新谋教授诞辰100周年[J]. 数学物理学报, 2010, 30(5): 1364-1376.
[6]	于卓熙, 王德辉, 史宁中. 带有误差变量的自回归模型的局部多项式估计[J]. 数学物理学报, 2010, 30(4): 984-999.
[7]	冯三营, 薛留根, 范承华. 非线性半参数回归模型中参数的经验似然置信域[J]. 数学物理学报, 2009, 29(5): 1338-1349.
[8]	李永明, 韦程东. 强混合误差回归函数小波估计的Berry-Esseen界[J]. 数学物理学报, 2009, 29(5): 1453-1463.
[9]	李元 ;杨益党. 带有随机设计的非参数回归模型的异方差小波检验[J]. 数学物理学报, 2007, 27(4): 727-740.
[10]	张尚立;覃红. 约束条件下线性模型协方差阵扰动的影响分析[J]. 数学物理学报, 2006, 26(4): 621-628.
[11]	潘光明, 胡舒合, 方利宝, 程正东. 半参数回归模型估计的平均相合性[J]. 数学物理学报, 2003, 23(5): 598-606.
[12]	陈明华. 完全与截尾样本时半参数回归模型估计的强相合性[J]. 数学物理学报, 1999, 19(5): 501-506.
[13]	胡舒合. 一类半参数回归模型的估计问题[J]. 数学物理学报, 1999, 19(5): 541-549.
[14]	陈明华. 固定设计下半参数回归模型的参数估计的Bootstrap的逼近[J]. 数学物理学报, 1999, 19(2): 121-129.
[15]	林路. 非线性模型中的拟似然估计和约束拟似然估计[J]. 数学物理学报, 1998, 18(S1): 133-138.