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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.

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Bibliographic Info

Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 09-2004.

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Length: 27 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:mtl:montec:09-2004

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Keywords: finite-state Markov chains; time reversibility; bayesian inference; hidden Markov models;

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References

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  1. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
  2. Scott S. L., 2002. "Bayesian Methods for Hidden Markov Models: Recursive Computing in the 21st Century," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 337-351, March.
  3. Chen, Yi-Ting & Chou, Ray Y. & Kuan, Chung-Ming, 2000. "Testing time reversibility without moment restrictions," Journal of Econometrics, Elsevier, vol. 95(1), pages 199-218, March.
  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. Melvin J. Hinich & Philip Rothman, . "A Frequency Domain Test of Time Reversibility," Working Papers 9706, East Carolina University, Department of Economics.
  6. Ramsey, James B & Rothman, Philip, 1996. "Time Irreversibility and Business Cycle Asymmetry," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(1), pages 1-21, February.
  7. Fong, Wai Mun, 2003. "Time reversibility tests of volume-volatility dynamics for stock returns," Economics Letters, Elsevier, vol. 81(1), pages 39-45, October.
  8. 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.
  9. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  10. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  11. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  12. Serge Darolles & Jean-Pierre Florens & Christian Gourieroux, 2000. "Kernel Based Nonlinear Canonical Analysis and Time Reversibility," Working Papers 2000-18, Centre de Recherche en Economie et Statistique.
  13. repec:fth:inseep:2000-18 is not listed on IDEAS
  14. Andrew Eckert, 2002. "Retail price cycles and response asymmetry," Canadian Journal of Economics, Canadian Economics Association, vol. 35(1), pages 52-77, February.
  15. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-99, May.
  16. William J. McCausland, 2004. "Using the BACC Software for Bayesian Inference," Computational Economics, Society for Computational Economics, vol. 23(3), pages 201-218, 04.
  17. 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.
  18. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
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Citations

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Cited by:
  1. Beare, Brendan, 2008. "Copulas and Temporal Dependence," University of California at San Diego, Economics Working Paper Series qt2880q2jq, Department of Economics, UC San Diego.
  2. Beare, Brendan K. & Seo, Juwon, 2012. "Time irreversible copula-based Markov Models," University of California at San Diego, Economics Working Paper Series qt31f8500p, Department of Economics, UC San Diego.
  3. Beare, Brendan K., 2009. "Copulas and Temporal Dependence," University of California at San Diego, Economics Working Paper Series qt87p829d4, Department of Economics, UC San Diego.
  4. McCAUSLAND, William, 2004. "Time Reversibility of Stationary Regular Finite State Markov Chains," Cahiers de recherche 2004-07, Universite de Montreal, Departement de sciences economiques.
  5. 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, vol. 21(1), pages 170-187, March.

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