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Time Reversibility of Stationary Regular Finite State Markov Chains

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  • McCAUSLAND, William

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, 2004. "Time Reversibility of Stationary Regular Finite State Markov Chains," Cahiers de recherche 2004-07, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2004-07
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    File URL: http://hdl.handle.net/1866/521
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    1. McCausland, William J., 2007. "Time reversibility of stationary regular finite-state Markov chains," Journal of Econometrics, Elsevier, vol. 136(1), pages 303-318, January.
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    13. Clements, Michael P & Krolzig, Hans-Martin, 2003. "Business Cycle Asymmetries: Characterization and Testing Based on Markov-Switching Autoregressions," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 196-211, January.
    14. Eckert, Andrew, 2003. "Retail price cycles and the presence of small firms," International Journal of Industrial Organization, Elsevier, vol. 21(2), pages 151-170, February.
    15. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
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    Cited by:

    1. 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.
    2. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    3. 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).
    4. McCausland, William J., 2007. "Time reversibility of stationary regular finite-state Markov chains," Journal of Econometrics, Elsevier, vol. 136(1), pages 303-318, January.
    5. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(5), pages 923-960, October.
    6. 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.
    7. 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.

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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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