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Estimation and inference in multivariate Markov chains

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  • João Nicolau
  • Flavio Riedlinger

Abstract

The literature of Markov chains has recently focused on modeling multiple categorical data sequences. The usual procedure for handling these multivariate Markov chains (MMC), with $$m$$ m categorical data and $$s$$ s states, consists of expanding the state space by considering $$m^{s}$$ m s new states. This model rapidly becomes intractable even with moderate values of $$m$$ m and $$s$$ s due to the excessive number of parameters to estimate. Ching and Fung ( 2002 ) found a way to cope with the intractability of the conventional MMC. They also suggested a method of estimation that proved to be inefficient. Zhu and Ching ( 2010 ) proposed another method of estimation based on minimizing the prediction error with equality and inequality restrictions. However, both these procedures treat the estimation problem as a mechanic method, without addressing the statistical inference problem. In this article we try to overcome this shortcoming and, at the same time, we propose a new approach to estimate MMC (under Ching et al. hypothesis) which avoids imposing equality and inequality restrictions on the parameters. We illustrate the model and the estimation method with two applications on financial time series data. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • João Nicolau & Flavio Riedlinger, 2015. "Estimation and inference in multivariate Markov chains," Statistical Papers, Springer, vol. 56(4), pages 1163-1173, November.
  • Handle: RePEc:spr:stpapr:v:56:y:2015:i:4:p:1163-1173
    DOI: 10.1007/s00362-014-0630-6
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    References listed on IDEAS

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    1. 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.
    2. McQueen, Grant & Thorley, Steven, 1991. "Are Stock Returns Predictable? A Test Using Markov Chains," Journal of Finance, American Finance Association, vol. 46(1), pages 239-263, March.
    3. Alireza Faraz & Erwin Saniga, 2011. "A unification and some corrections to Markov chain approaches to develop variable ratio sampling scheme control charts," Statistical Papers, Springer, vol. 52(4), pages 799-811, November.
    4. 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.
    5. Wai-Ki Ching & Michael K. Ng, 2006. "Markov Chains: Models, Algorithms and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-29337-0, December.
    6. Tzong-Ru Tsai & Wen-Pin Yen, 2011. "Exponentially weighted moving average control charts for three-level products," Statistical Papers, Springer, vol. 52(2), pages 419-429, May.
    7. Kosorok, Michael R., 2000. "Monte Carlo error estimation for multivariate Markov chains," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 85-93, January.
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    Cited by:

    1. 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).
    2. Bruno Damásio & João Nicolau, 2020. "Time Inhomogeneous Multivariate Markov Chains: Detecting and Testing Multiple Structural Breaks Occurring at Unknown," Working Papers REM 2020/0136, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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