似然比扫描法在长记忆时间序列均值多变点中的应用
Application of Likelihood Ratio Scanning Method in Multiple Mean Changes in Long Memory Time Series
DOI: 10.12677/HJDM.2019.92002, PDF,  被引量    国家自然科学基金支持
作者: 徐琼瑶*, 邢玉红：青海师范大学数学与统计学院，青海 西宁
关键词: 长记忆时间序列；均值多变点；似然比扫描统计量； Long Memory Time Series； Mean Change Points； Likelihood Ratio Scanning Statistics
摘要: 本文基于似然比扫描方法，研究分段平稳长记忆时间序列中的均值多变点问题，通过数值模拟发现，直接将似然比扫描方法应用于长记忆时间序列会导致对变点个数及位置的检测不准确。通过改变似然比扫描方法中似然函数参数的残差估计方法，提出了一种适合长记忆时间序列的似然比扫描方法，数值模拟和实际数据分析证明了改进后的方法的有效性和实用性。
Abstract: Based on likelihood ratio scanning method (LRSM), this paper studies the multiple change point problem of mean in piecewise stationary long memory time series. Through numerical simulation, it is found that applying the LRSM directly to long memory time series will lead to inaccurate detection of the number and location of change points. By revising the residual estimation method of likelihood function parameters in LRSM, a new LRSM is proposed which is suitable for long memory time series. The effectiveness and practicability of the improved method are proved by numerical simulation and actual data analysis.
文章引用：徐琼瑶, 邢玉红. 似然比扫描法在长记忆时间序列均值多变点中的应用[J]. 数据挖掘, 2019, 9(2): 9-17. https://doi.org/10.12677/HJDM.2019.92002

参考文献

[1] Page, E.S. (1955) A Test for a Change in a Parameter Occurring at an Unknown Point. Biometrika, 42, 523-527. [Google Scholar] [CrossRef] 
[2] 王欣, 尹留志, 方兆本. 异常交易行为的甄别研究[J]. 数理统计与管理, 2009, 28(4): 671-677.
[3] 张丕远, 王铮, 刘啸雷. 中国近2000年气候演变的阶段性[J]. 中国科学(B), 1994, 24(9): 998-1008.
[4] Staudacher, M., Telser, S., Amann, A., Hinterhuber, H. and Ritsch-Marte, M. (2005) A New Method for Change Point Detection Developed for On-Line Analysis of the Heart Beat Variability during Sleep. Physica A, 349, 582-596. [Google Scholar] [CrossRef] 
[5] Kokoszka, P. and Leipus, R. (2000) Change-Point Estimation in ARCH Models. Bernoulli, 6, 513-539. [Google Scholar] [CrossRef] 
[6] Kokoszka, P. and Leipus, R. (1998) Change-Point in the Mean of Dependent Observations. Statistics & Probability Letters, 40, 385-393. [Google Scholar] [CrossRef] 
[7] Kokoszka, P. and Leipus, R. (1999) Testing for Parameter Changes in ARCH Model. Lithuanian Mathematical Journal, 39, 182-195. [Google Scholar] [CrossRef] 
[8] Kim, S., Cho, S. and Lee, S. (2000) On the CUSUM Test for Parameter Changes in GARCH(1,1) Models. Communication in Statistics-Theory and Methods, 29,445-462. [Google Scholar] [CrossRef] 
[9] Lee, S., Tokutsu, Y. and Maekawa, K. (2004) The CUSUM Test for Parameter Change in Regression Models with ARCH Error. Journal of the Japanese Statistical Society, 34, 173-188. [Google Scholar] [CrossRef] 
[10] 马健琦, 陈占寿, 吕娜. 基于Sieve Bootstrap 方法的长记忆过程均值变点的检验[J]. 青海师范大学学报(自科版)，2017, 33(2): 34-38.
[11] 秦瑞兵, 田铮, 陈占寿. 独立随机序列均值多变点的非参数检验[J]. 应用概率统计, 2013, 29(5): 449-457.
[12] Chen, Z., Tian, Z., et al. (2012) Moving Ratio Test for Multiple Changes in Persistence. Journal of Systems Science & Complexity, 25, 582-593. [Google Scholar] [CrossRef] 
[13] Chen, Z., Jin, Z., Tian, Z., et al. (2012) Bootstrap Testing Multiple Changes in Persistence for a Heavy-Tailed Sequence. Computational Statistics & Data Analysis, 56, 2303-2316. [Google Scholar] [CrossRef] 
[14] Yao, Y.C. (1987) Approximating the Distribution of the Maximum Likelihood Estimate of the Change-Point in a Sequence of Independent Random Variables. The Annals of Statistics, 15, 1321-1328. [Google Scholar] [CrossRef] 
[15] Lavielle, M. and Ludena, C. (2000) The Multiple Change Points Problem for the Spectral Distribution. Bernoulii, 6, 845-869. [Google Scholar] [CrossRef] 
[16] Davis, R.A., Lee, T.C.M. and Rodriguez-Yam, G.A. (2006) Structural Break Estimation for Non-Stationary Time Series Models. Journal of the American Statistical Association, 101, 223-239. [Google Scholar] [CrossRef] 
[17] Killick, R., Fearnhead, P. and Eckley, I.A. (2012) Optimal Detection of Change Points with a Linear Computational Cost. Journal of the American Statistical Association, 107, 1590-1598. [Google Scholar] [CrossRef] 
[18] Vostrikova, L. (1981) Detecting Disorder in Multidimensional Random Processes. Soviet Mathematics, Doklady, 24, 55-59.
[19] Bai, J. (1997) Estimating Multiple Breaks One at a Time. Econometric Theory, 13, 315-352. [Google Scholar] [CrossRef] 
[20] Inclan, C. and Tiao, G.C. (1994) Use of Cumulative Sums of Squares for Retrospective Detection of Change of Variance. Journal of the American Statistical Association, 89, 913-923.
[21] Berkes, J., Gombay, E. and Horvath, L. (2009) Testing for Changes in the Covariance Structure of Linear Processes. Journal of Statistical Planning and Inference, 139, 2044-2063. [Google Scholar] [CrossRef] 
[22] Fryzlewicz, P. (2014) Wild Binary Segmentation for Multiple Change-Point Detection. The Annals of Statistics, 42, 2243-2281. [Google Scholar] [CrossRef] 
[23] Yau, C.Y. and Zhao, Z. (2016). Inference for Multiple Change Points in Time Series via Likelihood Ratio Scan Statistics. Journal of the Royal Statistical Society: Series B, 78, 895-916.[CrossRef] 

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