×

Multiple changepoint detection with partial information on changepoint times. (English) Zbl 1422.62286

Summary: This paper proposes a new minimum description length procedure to detect multiple changepoints in time series data when some times are a priori thought more likely to be changepoints. This scenario arises with temperature time series homogenization pursuits, our focus here. Our Bayesian procedure constructs a natural prior distribution for the situation, and is shown to estimate the changepoint locations consistently, with an optimal convergence rate. Our methods substantially improve changepoint detection power when prior information is available. The methods are also tailored to bivariate data, allowing changes to occur in one or both component series.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62C12 Empirical decision procedures; empirical Bayes procedures
62G10 Nonparametric hypothesis testing
62H12 Estimation in multivariate analysis

References:

[1] Aue, A. and Horváth, L. (2013). Structural Breaks in Time Series., Journal of Time Series Analysis 34 1-16. · Zbl 1274.62553 · doi:10.1111/j.1467-9892.2012.00819.x
[2] Bardwell, L. and Fearnhead, P. (2017). Bayesian Detection of Abnormal Segments in Multiple Time Series., Bayesian Analysis. · Zbl 1384.62286 · doi:10.1214/16-BA998
[3] Barry, D. and Hartigan, J. A. (1993). A Bayesian Analysis for Change Point Problems., Journal of the American Statistical Association 88 309-319. · Zbl 0775.62065
[4] Billingsley, P. (1995)., Probability and Measure, Third ed. John Wiley & Sons. · Zbl 0822.60002
[5] Brockwell, P. J. and Davis, R. A. (1991)., Time Series: Theory and Methods, Second ed. Springer-Verlag. · Zbl 0709.62080
[6] Carlin, B. P. and Louis, T. A. (2000)., Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall/CRC Boca Raton. · Zbl 1017.62005
[7] Caussinus, H. and Mestre, O. (2004). Detection and Correction of Artificial Shifts in Climate Series., Journal of the Royal Statistical Society: Series C (Applied Statistics) 53 405-425. · Zbl 1111.62365 · doi:10.1111/j.1467-9876.2004.05155.x
[8] Chan, N. H., Yau, C. Y. and Zhang, R.-M. (2014). Group LASSO for Structural Break Time Series., Journal of the American Statistical Association 109 590-599. · Zbl 1367.62251 · doi:10.1080/01621459.2013.866566
[9] Chernoff, H. and Zacks, S. (1964). Estimating the Current Mean of a Normal Distribution which is Subjected to Changes in Time., The Annals of Mathematical Statistics 35 999-1018. · Zbl 0218.62033 · doi:10.1214/aoms/1177700517
[10] Chib, S. (1998). Estimation and Comparison of Multiple Change-point Models., Journal of Econometrics 86 221-241. · Zbl 1045.62510 · doi:10.1016/S0304-4076(97)00115-2
[11] Cho, H. and Fryzlewicz, P. (2015). Multiple-change-point Detection for High Dimensional Time Series via Sparsified Binary Segamentation., Journal of the Royal Statistical Society: Series B (Statistical Methodology) 77 475-507. · Zbl 1414.62356 · doi:10.1111/rssb.12079
[12] Christensen, R. (2002)., Plane Answers to Complex Questions: The Theory of Linear Models. Springer. · Zbl 0992.62059
[13] Clyde, M. A. and George, E. I. (2004). Model Uncertainty., Statistical Science 19 81-94. · Zbl 1062.62044 · doi:10.1214/088342304000000035
[14] Davis, R. A., Lee, T. C. M. and Rodriguez-Yam, G. A. (2006). Structural Break Estimation for Nonstationary Time Series Models., Journal of the American Statistical Association 101 223-239. · Zbl 1118.62359 · doi:10.1198/016214505000000745
[15] Davis, R. A., Lee, T. C. M. and Rodriguez-Yam, G. A. (2008). Break Detection for a Class of Nonlinear Time Series Models., Journal of Time Series Analysis 29 834-867. · Zbl 1199.62006 · doi:10.1111/j.1467-9892.2008.00585.x
[16] Davis, R. A. and Yau, C. Y. (2013). Consistency of Minimum Description Length Model Selection for Piecewise Stationary Time Series Models., Electronic Journal of Statistics 7 381-411. · Zbl 1337.62254 · doi:10.1214/13-EJS769
[17] Du, C., Kao, C.-L. M. and Kou, S. C. (2016). Stepwise Signal Extraction via Marginal Likelihood., Journal of the American Statistical Association 111 314-330.
[18] Fearnhead, P. (2006). Exact and Efficient Bayesian Inference for Multiple Changepoint Problems., Statistical Computing 16 203-213.
[19] Fearnhead, P. and Vasileiou, D. (2009). Bayesian Analysis of Isochores., Journal of the American Statistical Association 104 132-141. · Zbl 1388.62319 · doi:10.1198/jasa.2009.0009
[20] Fryzlewicz, P. (2014). Wild Binary Segmentation for Multiple Change-Point Detection., Annals of Statistics 42 2243-2281. · Zbl 1302.62075 · doi:10.1214/14-AOS1245
[21] Fryzlewicz, P. and Subba Rao, S. (2014). Multiple-Change-Point Detection for Auto-Regressive Conditional Heteroscedastic Processes., Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76 903-924. · Zbl 1411.62248 · doi:10.1111/rssb.12054
[22] García-Donato, G. and Martínez-Beneito, M. A. (2013). On Sampling Strategies in Bayesian Variable Selection Problems with Large Model Spaces., Journal of the American Statistical Association 108 340-352. · Zbl 06158347
[23] George, E. I. and McCulloch, R. E. (1997). Approaches for Bayesian Variable Selection., Statistics Sinica 7 339-373. · Zbl 0884.62031
[24] Giordani, P. and Kohn, R. (2008). Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models., Journal of Business and Economic Statistics 26 66-77.
[25] Girón, J., Moreno, E. and Casella, G. (2007). Objective Bayesian Analysis of Multiple Changepoints for Linear Models., Bayesian Statistics 8. · Zbl 1252.62019
[26] Green, J. Peter (1995). Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination., Biometrika 82 711-732. · Zbl 0861.62023 · doi:10.1093/biomet/82.4.711
[27] Grünwald, P. D. (2007)., The Minimum Description Length Principle. The MIT Press.
[28] Hannart, A. and Naveau, P. (2012). An Improved Bayesian Information Criterion for Multiple Change-point Models., Technometrics 54 256-268.
[29] Hansen, M. H. and Yu, B. (2001). Model Selection and the Principle of Minimum Description Length., Journal of the American Statistical Association 96 746-774. · Zbl 1017.62004 · doi:10.1198/016214501753168398
[30] Harville, D. A. (2008)., Matrix Algebra From a Statistician’s Perspective. Springer-Verlag. · Zbl 1142.15001
[31] Hewaarachchi, A., Li, Y., Lund, R. and Rennie, J. (2017). Homogenization of Daily Temperature Data., Journal of Climate 30 985-999.
[32] Kass, R. E. and Raftery, A. E. (1995). Bayes Factors., Journal of the American Statistical Association 90 773-795. · Zbl 0846.62028 · doi:10.1080/01621459.1995.10476572
[33] Killick, R., Fearnhead, P. and Eckley, I. A. (2012). Optimal Detection of Changepoints With a Linear Computational Cost., Journal of the American Statistical Association 107 1590-1598. · Zbl 1258.62091 · doi:10.1080/01621459.2012.737745
[34] Kirch, C., Muhsal, B. and Ombao, H. (2015). Detection of Changes in Multivariate Time Series with Application to EEG Data., Journal of the American Statistical Association 110 1197-1216. · Zbl 1378.62072 · doi:10.1080/01621459.2014.957545
[35] Li, S. and Lund, R. (2012). Multiple Changepoint Detection via Genetic Algorithms., Journal of Climate 25 674-686.
[36] Li, Y. and Lund, R. (2015). Multiple Changepoint Detection Using Metadata., Journal of Climate 28 4199-4216.
[37] Li, F. and Zhang, N. R. (2010). Bayesian Variable Selection in Structured High-Dimensional Covariate Spaces with Applications in Genomics., Journal of the American Statistical Association 105 1202-1214. · Zbl 1390.62027 · doi:10.1198/jasa.2010.tm08177
[38] Liu, G., Shao, Q., Lund, R. and Woody, J. (2016). Testing for Seasonal Means in Time Series Data., Environmetrics 27 198-211. · Zbl 1525.62170
[39] Lu, Q., Lund, R. and Lee, T. C. M. (2010). An MDL Approach to the Climate Segmentation Problem., The Annals of Applied Statistics 4 299-319. · Zbl 1189.62180 · doi:10.1214/09-AOAS289
[40] Lund, R. B., Wang, X. L., Reeves, J., Lu, Q. Q., Gallagher, C. M. and Feng, Y. (2007). Changepoint Detection in Periodic and Autocorrelated Time Series., Journal of Climate 20 5178-5190.
[41] Ma, T. F. and Yau, C. Y. (2016). A Pairwise Likelihood-based Approach for Changepoint Detection in Multivariate Time Series Models., Biometrika 103 409-421. · Zbl 1499.62314 · doi:10.1093/biomet/asw002
[42] Menne, M. J. and Williams Jr, C. N. (2005). Detection of Undocumented Changepoints Using Multiple Test Statistics and Composite Reference Series., Journal of Climate 18 4271-4286.
[43] Mitchell, J. M. (1953). On the Causes of Instrumentally Observed Secular Temperature Trends., Journal of Meteorology 10 244-261.
[44] Niu, Y. S., Hao, N. and Zhang, H. (2016). Multiple Change-Point Detection: A Selective Overview., Statistical Science 31 611-623. · Zbl 1442.62170 · doi:10.1214/16-STS587
[45] Pein, F., Sieling, H. and Munk, A. (2017). Heterogeneous Change Point Inference., Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79 1207-1227. · Zbl 1373.62258 · doi:10.1111/rssb.12202
[46] Preuss, P., Puchstein, R. and Dette, H. (2015). Detection of Multiple Structural Breaks in Multivariate Time Series., Journal of the American Statistical Association 110 654-668. · Zbl 1373.62454 · doi:10.1080/01621459.2014.920613
[47] Risanen, J. (1989)., Stochastic Complexity in Statistical Inquiry 511. World Scientific, Singapore. · Zbl 0800.68508
[48] Schwarz, G. (1978). Estimating the Dimension of a Model., The Annals of Statistics 6 461-464. · Zbl 0379.62005 · doi:10.1214/aos/1176344136
[49] Scott, J. and Berger, J. (2010). Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-selection Problem., The Annals of Statistics 38 2587-2619. · Zbl 1200.62020 · doi:10.1214/10-AOS792
[50] Shannon, C. E. (1948). A Mathematical Theory of Communication., Bell System Technical Journal 27 623. · Zbl 1154.94303 · doi:10.1002/j.1538-7305.1948.tb01338.x
[51] Shao, X. and Zhang, X. (2010). Testing for Change Points in Time Series., Journal of the American Statistical Association 105 1228-1240. · Zbl 1390.62184 · doi:10.1198/jasa.2010.tm10103
[52] Wilks, D. S. (2011)., Statistical Methods in the Atmospheric Sciences. Academic Press.
[53] Yao, Y.-C. (1984). Estimation of a Noisy Discrete-Time Step Function: Bayes and Empirical Bayes Approaches., The Annals of Statistics 12 1434-1447. · Zbl 0551.62069 · doi:10.1214/aos/1176346802
[54] Yao, Y.-C. (1988). Estimating the Number of Change-Points via Schwarz’ Criterion., Statistics & Probability Letters 6 181-189. · Zbl 0642.62016 · doi:10.1016/0167-7152(88)90118-6
[55] Yau, C. Y., Tang, C. M. and Lee, T. C. M. (2015). Estimation of Multiple-Regime Threshold Autoregressive Models with Structural Breaks., Journal of the American Statistical Association 110 1175-1186. · Zbl 1373.62461 · doi:10.1080/01621459.2014.954706
[56] 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 (Statistical Methodology) 78 895-916. · Zbl 1414.62386 · doi:10.1111/rssb.12139
[57] Zhang, N. R. and Siegmund, D. O. (2007). A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data., Biometrics 63 22-32. · Zbl 1206.62174 · doi:10.1111/j.1541-0420.2006.00662.x
[58] Zhang, N. R. and Siegmund, D. O. (2012). Model Selection for High-Dimensional, Multi-Sequence Change-Point Problems., Statistica Sinica 1507-1538. · Zbl 1264.62079
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.