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Time inhomogeneous multivariate Markov chains: Detecting and testing multiple structural breaks occurring at unknown dates

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  • Damásio, Bruno
  • Nicolau, João

Abstract

Markov chain models are used in several applications and different areas of study. A Markov chain model is usually assumed to be homogeneous in the sense that the transition probabilities are time-invariant. Yet, ignoring the inhomogeneous nature of a stochastic process by disregarding the presence of structural breaks can lead to misleading conclusions. Several methodologies are currently proposed for detecting structural breaks in a Markov chain. However, these methods have some limitations: namely they can only test directly for the presence of a single structural break. This paper proposes a new methodology for detecting and testing the presence of multiple structural breaks in a Markov chain occurring at unknown dates.

Suggested Citation

  • Damásio, Bruno & Nicolau, João, 2024. "Time inhomogeneous multivariate Markov chains: Detecting and testing multiple structural breaks occurring at unknown dates," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924000298
    DOI: 10.1016/j.chaos.2024.114478
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    1. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    2. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    3. João Nicolau, 2014. "A New Model for Multivariate Markov Chains," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1124-1135, December.
    4. Kejriwal, Mohitosh & Perron, Pierre, 2010. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 503-522.
    5. Maskawa, Jun-ichi, 2003. "Multivariate Markov chain modeling for stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 317-322.
    6. Bruce Bukiet & Elliotte Rusty Harold & José Luis Palacios, 1997. "A Markov Chain Approach to Baseball," Operations Research, INFORMS, vol. 45(1), pages 14-23, February.
    7. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    8. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    9. Tan, Baris & Yilmaz, Kamil, 2002. "Markov chain test for time dependence and homogeneity: An analytical and empirical evaluation," European Journal of Operational Research, Elsevier, vol. 137(3), pages 524-543, March.
    10. João Nicolau & Flavio Riedlinger, 2015. "Estimation and inference in multivariate Markov chains," Statistical Papers, Springer, vol. 56(4), pages 1163-1173, November.
    11. Jushan Bai, 2000. "Vector Autoregressive Models with Structural Changes in Regression Coefficients and in Variance-Covariance Matrices," Annals of Economics and Finance, Society for AEF, vol. 1(2), pages 303-339, November.
    12. Shamshad, A. & Bawadi, M.A. & Wan Hussin, W.M.A. & Majid, T.A. & Sanusi, S.A.M., 2005. "First and second order Markov chain models for synthetic generation of wind speed time series," Energy, Elsevier, vol. 30(5), pages 693-708.
    13. Asadabadi, Mehdi Rajabi, 2017. "A customer based supplier selection process that combines quality function deployment, the analytic network process and a Markov chain," European Journal of Operational Research, Elsevier, vol. 263(3), pages 1049-1062.
    14. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, December.
    15. Nicolau, João, 2017. "A simple nonparametric method to estimate the expected time to cross a threshold," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 146-152.
    16. Andre Berchtold, 2001. "Estimation in the Mixture Transition Distribution Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 379-397, July.
    17. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 114(2), pages 261-295, June.
    18. Bruce E. Hansen, 2001. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 117-128, Fall.
    19. Rappoport, Peter & Reichlin, Lucrezia, 1989. "Segmented Trends and Non-stationary Time Series," Economic Journal, Royal Economic Society, vol. 99(395), pages 168-177, Supplemen.
    20. Gangloff, Hugo & Morales, Katherine & Petetin, Yohan, 2023. "Deep parameterizations of pairwise and triplet Markov models for unsupervised classification of sequential data," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    21. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    22. Adrian Raftery & Simon Tavaré, 1994. "Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 179-199, March.
    23. Jushan Bai & Robin L. Lumsdaine & James H. Stock, 1998. "Testing For and Dating Common Breaks in Multivariate Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 395-432.
    24. Ling, Shiqing, 2016. "Estimation Of Change-Points In Linear And Nonlinear Time Series Models," Econometric Theory, Cambridge University Press, vol. 32(2), pages 402-430, April.
    25. García Cabello, Julia, 2017. "The future of branch cash holdings management is here: New Markov chains," European Journal of Operational Research, Elsevier, vol. 259(2), pages 789-799.
    26. Polansky, Alan M., 2007. "Detecting change-points in Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6013-6026, August.
    27. Tsiliyannis, Christos Aristeides, 2018. "Markov chain modeling and forecasting of product returns in remanufacturing based on stock mean-age," European Journal of Operational Research, Elsevier, vol. 271(2), pages 474-489.
    28. Eric Fung & Tak Siu, 2012. "A Flexible Markov Chain Approach for Multivariate Credit Ratings," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 135-143, February.
    29. Damásio, Bruno & Louçã, Francisco & Nicolau, João, 2018. "The changing economic regimes and expected time to recover of the peripheral countries under the euro: A nonparametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 524-533.
    30. Tak-Kuen Siu & Wai-Ki Ching & S. Eric Fung & Michael Ng, 2005. "On a multivariate Markov chain model for credit risk measurement," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 543-556.
    31. Jin-Guo Xian & Dong Han & Jian-Qi Yu, 2016. "Online change detection of Markov chains with unknown post-change transition probabilities," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 597-611, February.
    32. Kristi Kuljus & Jüri Lember, 2023. "Pairwise Markov Models and Hybrid Segmentation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-32, June.
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