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Detection of multiple changes in a sequence of dependent variables

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  • Lavielle, Marc

Abstract

We present some results of convergence for a minimum contrast estimator in a problem of change-points estimation. Here, we consider that the changes affect the marginal distribution of a sequence of random variables. We only consider parametric models, but the results are obtained under very general conditions. We show that the estimated configuration of changes converges to the true configuration, and we show that the rate of convergence does not depend on the dependance structure of the process: we obtain the same rate for strongly mixing and strongly dependent processes. When the number of changes is unknown, it is estimated by minimizing a penalized contrast function. Some examples of application to real data are given.

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  • Lavielle, Marc, 1999. "Detection of multiple changes in a sequence of dependent variables," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 79-102, September.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:1:p:79-102
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    1. Kim, H. J., 1994. "Likelihood Ratio and Cumulative Sum Tests for a Change-Point in Linear Regression," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 54-70, October.
    2. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
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    1. Elena Andreou, 2004. "The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 290-318.
    2. Erico N de Souza & Kristina Boerder & Stan Matwin & Boris Worm, 2016. "Improving Fishing Pattern Detection from Satellite AIS Using Data Mining and Machine Learning," PLOS ONE, Public Library of Science, vol. 11(7), pages 1-20, July.
    3. Piet Jong & Sonia Mazzi, 2001. "Modeling and Smoothing Unequally Spaced Sequence Data," Statistical Inference for Stochastic Processes, Springer, vol. 4(1), pages 53-71, January.
    4. Salvatore Fasola & Vito M. R. Muggeo & Helmut Küchenhoff, 2018. "A heuristic, iterative algorithm for change-point detection in abrupt change models," Computational Statistics, Springer, vol. 33(2), pages 997-1015, June.
    5. Bouzebda, Salim & Ferfache, Anouar Abdeldjaoued, 2023. "Asymptotic properties of semiparametric M-estimators with multiple change points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    6. Jean-Marc Bardet & Imen Kammoun & Veronique Billat, 2012. "A new process for modeling heartbeat signals during exhaustive run with an adaptive estimator of its fractal parameters," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1331-1351, December.
    7. Kirman, Alan & Teyssiere, Gilles, 2005. "Testing for bubbles and change-points," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 765-799, April.
    8. Roberts, Leigh, 2014. "Consistent estimation of breakpoints in time series, with application to wavelet analysis of Citigroup returns," Working Paper Series 18815, Victoria University of Wellington, School of Economics and Finance.
    9. Cosimo Petracchi, 2021. "The Mussa Puzzle: A Generalization," Working Papers 2021-001, Brown University, Department of Economics.
    10. Shi, Xiaoping & Wu, Yuehua & Miao, Baiqi, 2009. "Strong convergence rate of estimators of change point and its application," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 990-998, February.
    11. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
    12. Chen, Shuo & Hong, Don & Shyr, Yu, 2007. "Wavelet-based procedures for proteomic mass spectrometry data processing," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 211-220, September.
    13. Mohamed Boutahar & Mustapha Belkhouja, 2007. "Le Changement Structurel Dans Un Environnement Mémoire Longue," Working Papers halshs-00352610, HAL.
    14. Davies, Laurie & Höhenrieder, Christian & Krämer, Walter, 2012. "Recursive computation of piecewise constant volatilities," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3623-3631.
    15. Mondher Bellalah & Marc Lavielle, 2002. "A Decomposition of Empirical Distributions with Applications to the Valuation of Derivative Assets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(2), pages 99-130, June.
    16. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection," LSE Research Online Documents on Economics 103430, London School of Economics and Political Science, LSE Library.
    17. Petracchi, Cosimo, 2022. "The Mussa puzzle: A generalization," European Economic Review, Elsevier, vol. 149(C).
    18. Siu-Tong Au & Rong Duan & Siamak Hesar & Wei Jiang, 2010. "A framework of irregularity enlightenment for data pre-processing in data mining," Annals of Operations Research, Springer, vol. 174(1), pages 47-66, February.
    19. Fontaine, Charles & Frostig, Ron D. & Ombao, Hernando, 2020. "Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials," Econometrics and Statistics, Elsevier, vol. 15(C), pages 85-103.
    20. Tang, Huaizhi & Yun, Wenju & Liu, Wenping & Sang, Lingling, 2019. "Structural changes in the development of China’s farmland consolidation in 1998–2017: Changing ideas and future framework," Land Use Policy, Elsevier, vol. 89(C).
    21. Gabriela Ciuperca, 2011. "Estimating nonlinear regression with and without change-points by the LAD method," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 717-743, August.
    22. Pan, Jianmin & Chen, Jiahua, 2006. "Application of modified information criterion to multiple change point problems," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2221-2241, November.

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