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Time Reversibility of Stationary Regular Finite State Markov Chains

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  • McCAUSLAND, William J.

Abstract

We propose an alternate parameterization of stationary regular finite-state Markov chains, and a decomposition of the parameter into time reversible and time irreversible parts. We demonstrate some useful properties of the decomposition, and propose an index for a certain type of time irreversibility. Two empirical examples illustrate the use of the proposed parameter, decomposition and index. One involves observed states; the other, latent states.

Suggested Citation

  • McCAUSLAND, William J., 2004. "Time Reversibility of Stationary Regular Finite State Markov Chains," Cahiers de recherche 09-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:09-2004
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    References listed on IDEAS

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    Cited by:

    1. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    2. MacDonald, Iain L. & Pienaar, Etienne A.D., 2021. "Fitting a reversible Markov chain by maximum likelihood: Converting an awkwardly constrained optimization problem to an unconstrained one," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    3. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(5), pages 923-960, October.
    4. J. Besag & D. Mondal, 2013. "Exact Goodness-of-Fit Tests for Markov Chains," Biometrics, The International Biometric Society, vol. 69(2), pages 488-496, June.
    5. Yong Chen & Jianmin Chen, 2011. "On the Imbedding Problem for Three-State Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues," Journal of Theoretical Probability, Springer, vol. 24(4), pages 928-938, December.
    6. McCausland, William J., 2007. "Time reversibility of stationary regular finite-state Markov chains," Journal of Econometrics, Elsevier, vol. 136(1), pages 303-318, January.
    7. Davide Di Cecco, 2012. "Conditional exact tests for Markovianity and reversibility in multiple categorical sequences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 170-187, March.

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    More about this item

    Keywords

    finite-state Markov chains; time reversibility; bayesian inference; hidden Markov models;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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