Skip to main content
SpringerLink
Log in

Multipartition model for multiple change point identification

  • Original paper
  • Published:
TEST Aims and scope Submit manuscript

Abstract

The product partition model (PPM) is widely used for detecting multiple change points. Because changes in different parameters may occur at different times, the PPM fails to identify which parameters experienced the changes. To solve this limitation, we introduce a multipartition model to detect multiple change points occurring in several parameters. It assumes that changes experienced by each parameter generate a different random partition along the time axis, which facilitates identifying those parameters that changed and the time when they do so. We apply our model to detect multiple change points in Normal means and variances. Simulations and data illustrations show that the proposed model is competitive and enriches the analysis of change point problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Aminikhanghahi S, Cook DJ (2017) A survey of methods for time series change point detection. Knowl Inf Syst Int J 51(2):339–367

    Article  Google Scholar 

  • Bai J, Perron P (2003) Computation and analysis of multiple structural change models. J Appl Economet 18(1):1–22

    Article  Google Scholar 

  • Barry D, Hartigan JA (1992) Product partition models for change point problems. Ann Stat 20(1):260–279

    Article  MathSciNet  MATH  Google Scholar 

  • Barry D, Hartigan JA (1993) A Bayesian analysis for change point problems. J Am Stat Assoc 88(421):309–319

    MathSciNet  MATH  Google Scholar 

  • Chen J, Gupta A (2000) Parametric statistical change point analysis. Springer, Berlin

    Book  MATH  Google Scholar 

  • Chen YT, Chiou JM, Huang TM (2021) Greedy segmentation for a functional data sequence. J Am Stat Assoc 10(1080/01621459):1963261

    Google Scholar 

  • Chib S (1998) Estimation and comparison of multiple change-point models. J Econom 86(2):221–241

    Article  MathSciNet  MATH  Google Scholar 

  • Eddelbuettel D (2013) Seamless R and C++ Integration with Rcpp. Springer, New York (ISBN 978-1-4614-6867-7)

    Book  MATH  Google Scholar 

  • Erdman C, Emerson JW (2007) bcp: an r package for performing a Bayesian analysis of change point problems. J Stat Softw 23(3):1–13

    Article  Google Scholar 

  • Fearnhead P (2006) Exact and efficient Bayesian inference for multiple changepoint problems. Stat Comput 16(2):203–213

    Article  MathSciNet  Google Scholar 

  • Fearnhead P, Liu Z (2007) On-line inference for multiple changepoint problems. J R Stat Soc Ser B (Statistical Methodology) 69(4):589–605

    Article  MathSciNet  MATH  Google Scholar 

  • Fearnhead P, Liu Z (2011) Efficient Bayesian analysis of multiple changepoint models with dependence across segments. Stat Comput 21(2):217–229

    Article  MathSciNet  MATH  Google Scholar 

  • Fearnhead P, Rigaill G (2019) Changepoint detection in the presence of outliers. J Am Stat Assoc 114(525):169–183

    Article  MathSciNet  MATH  Google Scholar 

  • Ferreira JA, Loschi RH, Costa MA (2014) Detecting changes in time series: a product partition model with across-cluster correlation. Signal Process 96:212–227

    Article  Google Scholar 

  • García EC, Gutiérrez-Peñ E (2019) Nonparametric product partition models for multiple change-points analysis. Commun Stat Simul Comput 48(7):1922–1947

  • Garcia R, Perron P (1996) An analysis of the real interest rate under regime shifts. Rev Econ Stat 78(1):111–125

    Article  Google Scholar 

  • Gelman A, Rubin DB (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4):457–472

    Article  MATH  Google Scholar 

  • Hartigan JA (1990) Partition models. Commun Stat Theory Methods 19(8):2745–2756

    Article  MathSciNet  Google Scholar 

  • Horváth L, Rice G (2014) Extensions of some classical methods in change point analysis. TEST 23(2):219–255

    Article  MathSciNet  MATH  Google Scholar 

  • Jin H, Yin G, Yuan B et al (2022) Bayesian hierarchical model for change point detection in multivariate sequences. Technometrics 64(2):177–186

    Article  MathSciNet  Google Scholar 

  • Loschi RH, Cruz FR (2005) Extension to the product partition model: computing the probability of a change. Comput Stat Data Anal 48(2):255–268

    Article  MathSciNet  MATH  Google Scholar 

  • Loschi RH, Bastos LS, Iglesias PL (2005) Identifying volatility clusters using the ppm: a sensitivity analysis. Comput Econ 24(4):305–319

    Article  MATH  Google Scholar 

  • Martínez AF, Mena RH (2014) On a nonparametric change point detection model in Markovian regimes. Bayesian Anal 9(4):823–858

    Article  MathSciNet  MATH  Google Scholar 

  • Monteiro JV, Assunçao RM, Loschi RH (2011) Product partition models with correlated parameters. Bayesian Anal 6(4):691–726

    Article  MathSciNet  MATH  Google Scholar 

  • Niu YS, Hao N, Zhang H (2016) Multiple change-point detection: a selective overview. Stat Sci 31(4):611–623

    Article  MathSciNet  MATH  Google Scholar 

  • Nyamundanda G, Hegarty A, Hayes K (2015) Product partition latent variable model for multiple change-point detection in multivariate data. J Appl Stat 42(11):2321–2334

    Article  MathSciNet  MATH  Google Scholar 

  • Ogunniran AJ, Adekeye KS, Adewara JA et al (2021) A review of change point estimation methods for process monitoring. Appl Comput Math 10(3):69–75

    Article  Google Scholar 

  • Peluso S, Chib S, Mira A (2019) Semiparametric multivariate and multiple change-point modeling. Bayesian Anal 14(3):727–751

    Article  MathSciNet  MATH  Google Scholar 

  • Quinlan JJ, Page GL, Castro LM (2022) Joint random partition models for multivariate change point analysis. Bayesian Anal 1:1–28

    Article  Google Scholar 

  • Tartakovsky A, Nikiforov I, Basseville M (2020) Sequential analysis hypothesis testing and changepoint detection. Chapman & Hall, UK

    MATH  Google Scholar 

  • Truong C, Oudre L, Vayatis N (2020) Selective review of offline change point detection methods. Signal Process 167(107):299

    Google Scholar 

  • Van den Burg GJJ, Williams CKI (2020) An evaluation of change point detection algorithms. arXiv preprint https://arxiv.org/abs/2003.06222

  • Van Dyk DA, Park T (2008) Partially collapsed Gibbs samplers: theory and methods. J Am Stat Assoc 103(482):790–796

    Article  MathSciNet  MATH  Google Scholar 

  • Wyse J, Friel N, Rue H (2011) Approximate simulation-free bayesian inference for multiple changepoint models with dependence within segments. Bayesian Anal 6(4):501–528

    Article  MathSciNet  MATH  Google Scholar 

  • Yao YC (1984) Estimation of a noisy discrete-time step function: bayes and empirical bayes approaches. Ann Stat 12(4):1434–1447

    Article  MathSciNet  MATH  Google Scholar 

  • Yu X, Cheng Y (2022) A comprehensive review and comparison of cusum and change-point-analysis methods to detect test speededness. Multivar Behav Res 57(1):112–133

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the editors and anonymous referees whose comments and suggestions have contributed to improve this paper. We also thank Stefano Peluso for making code to fit the DPM19 model freely available.

Funding

This work was partially funded by Coordenação de Aperfeiçoamento de Pessoal de Ensino Superior (CAPES), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, 405025/2021-1, 304268/2021-6, 301627/2017-7) and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG, PPM-00243-18). Additional support for this work was obtained from grants Fondecyt 1180034, 1220017 and ANID - Millennium Science Initiative Program - NCN17_059.

Author information

Author notes

  1. All the authors have contributed equally to this work.

Authors and Affiliations

  1. Depto. de Estatística, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Ricardo C. Pedroso & Rosangela H. Loschi

  2. Depto. de Estadística, Pontificia Universidad Católica de Chile and Millennium Nucleus Center for the Discovery of Structures in Complex Data, Santiago, Chile

    Fernando Andrés Quintana

Authors
  1. Ricardo C. Pedroso
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rosangela H. Loschi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fernando Andrés Quintana
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ricardo C. Pedroso.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 3498 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pedroso, R.C., Loschi, R.H. & Quintana, F.A. Multipartition model for multiple change point identification. TEST 32, 759–783 (2023). https://doi.org/10.1007/s11749-023-00851-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11749-023-00851-4

Keywords

Mathematics Subject Classification

Search

Navigation