## Change-Point Problems

*27 Feb 2017 16:30*

Suppose you have a time series which has some (stochastic) property you're interested in, say its expected value or its variance. You think this is usually constant, but that if it does change, it does so abruptly. You would like to know if and when it changes, and perhaps to localize the time when it did. You now have a change-point problem.

See also: Time Series; Non-Stationary Forecasting; Filtering and State Estimation

- Recommended:
- Sylvain Arlot and Alain Celisse, "Segmentation of the mean of heteroscedastic data via cross-validation", Statistics and Computing
**21**(2011): 613--632, arxiv:0902.3977 [MATLAB code] - Emily B. Fox, Erik B. Sudderth, Michael I. Jordan, Alan S. Willsky,
"A sticky HDP-HMM with application to speaker diarization",
Annals of Applied Statistics
**5**(2011): 1020--1056, arxiv:0905.2592 - Daniil Ryabko and Boris Ryabko, "Testing Statistical Hypotheses
About Ergodic
Processes", arxiv:0804.0510
[Appears to be the same as their "Nonparametric Statistical Inference for
Ergodic
Processes", IEEE
Transactions on Information Theory
**56**(2010): 1430--1435 - Wenguang Sun, T. Tony Cai, "Large-scale multiple testing under dependence", Journal of the Royal Statistical
Society B
**71**(2008): 393--424 - Albert Vexler, "Martingale Type Statistics Applied to Change Point
Detection", Communications in Statistics - Theory and Methods
**37**(2008): 1207--1224

- To read:
- Alexander Aue and Lajos Horváth, "Structural breaks in time series", Journal of Time Series Analysis
**forthcoming (2012)** **Boris Brodsky and Boris Darkhovsky, "Sequential change-point detection for mixing random sequences under composite hypotheses", Statistical Inference for Stochastic Processes****11**(2008): 35--54**S. Camargo, S. M. Duarte Quieros and C. Anteneodo, "Nonparametric segmentation of nonstationary time series", Physical Review E****84**(2011): 046702**Cheng-Der Fuh**- "SPRT and CUSUM in hidden Markov models",
Annals of Statistics
**31**(2003): 942--977 - "Asymptotic operating characteristics of an optimal
change point detection in hidden Markov models", Annals of
Statistics
**32**(2004): 2305--2339 = math.ST/0503682

- "SPRT and CUSUM in hidden Markov models",
Annals of Statistics
**Samir Ben Hariz, Jonathan J. Wylie, Qiang Zhang, "Optimal rate of convergence for nonparametric change-point estimators for nonstationary sequences", Annals of Statistics****35**(2007): 1802--1826, arxiv:0710.4217**Heping He and Thomas A. Severini, "Asymptotic properties of maximum likelihood estimators in models with multiple change points", Bernoulli****16**(2010): 759--779, arxiv:1102.5224**C. T. Jose, B. Ismail, S. Jayasekhar, "Trend, Growth Rate, and Change Point Analysis: A Data Driven Approach", Communications in Statistics: Simulation and Computation****37**(2008): 498--506**Azadeh Khaleghi, Daniil Ryabko, "Multiple Change-Point Estimation in Stationary Ergodic Time-Series", arxiv:1203.1515****Shiqing Ling, "Testing for change points in time series models and limiting theorems for NED sequences", Annals of Statistics****35**(2007): 1213--1237, arxiv:0708.2369**George V. Moustakides, "Sequential change detection revisited", arxiv:0804.0741 = Annals of Statistics****36**(2008): 787--807**Chun Yip Yau and Richard A. Davis, "Likelihood inference for discriminating between long-memory and change-point models", Journal of Time Series Analysis****33**(2012): 649--664