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A Review Of The Estimation Of Transition Probabilities In Markov Chains

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  • Dent, Warren Thomas
  • Ballintine, Richard

Abstract

A chronological review of the development of estimation procedures for unknown constant Markovian transition probabilities is presented with emphasis on applications involving the availability of macrodata, as opposed to microdata. Monte Carlo results comparing various estimation methods are analysed and several suggestions for estimating non-stationary probabilities are made.

Suggested Citation

  • Dent, Warren Thomas & Ballintine, Richard, 1971. "A Review Of The Estimation Of Transition Probabilities In Markov Chains," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 15(2), pages 1-13, August.
    • Handle: RePEc:ags:ajaeau:22286
    DOI: 10.22004/ag.econ.22286
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    References listed on IDEAS

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    1. Kelley, Allen C & Weiss, Leonard W, 1969. "Markov Processes and Economic Analysis: The Case of Migration," Econometrica, Econometric Society, vol. 37(2), pages 280-297, April.
    2. M. C. Hallberg, 1969. "Projecting the Size Distribution of Agricultural Firms—An Application of a Markov Process with Non-Stationary Transition Probabilities," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 51(2), pages 289-302.
    3. Timothy McGuire, 1969. "More on least squares estimation of the transition matrix in a stationary first-order markov process from sample proportions data," Psychometrika, Springer;The Psychometric Society, vol. 34(3), pages 335-345, September.
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    5. T. C. Lee & G. G. Judge & T. Takayama, 1965. "On Estimating the Transition Probabilities of a Markov Process," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 47(3), pages 742-762.
    6. George Miller, 1952. "Finite markov processes in psychology," Psychometrika, Springer;The Psychometric Society, vol. 17(2), pages 149-167, June.
    7. Krenz, Ronald D., 1964. "Projection of Farm Numbers for North Dakota With Markov Chains," Journal of Agricultural Economics Research, United States Department of Agriculture, Economic Research Service, vol. 16(3), pages 1-7, July.
    8. Richard Kao, 1953. "Note on Miller's “Finite Markov Processes in Psychology”," Psychometrika, Springer;The Psychometric Society, vol. 18(3), pages 241-243, September.
    9. Judge, George G. & Swanson, E.R., 1962. "Markov Chains: Basic Concepts And Suggested Uses In Agricultural Economics," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 6(2), pages 1-13, December.
    10. T. C. Lee & G. G. Judge & R. L. Cain, 1969. "A Sampling Study of the Properties of Estimators of Transition Probabilities," Management Science, INFORMS, vol. 15(7), pages 374-398, March.
    11. H. Theil & Guido Rey, 1966. "A Quadratic Programming Approach to the Estimation of Transition Probabilities," Management Science, INFORMS, vol. 12(9), pages 714-721, May.
    12. Dryden, Myles M, 1969. "Share Price Movements: A Markovian Approach," Journal of Finance, American Finance Association, vol. 24(1), pages 49-60, March.
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    Cited by:

    1. Villacorta, Pablo J. & Verdegay, José L., 2016. "FuzzyStatProb: An R Package for the Estimation of Fuzzy Stationary Probabilities from a Sequence of Observations of an Unknown Markov Chain," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i08).
    2. Libbin, James D., 1982. "Projections of US farm numbers by Markov processes," ISU General Staff Papers 198201010800008508, Iowa State University, Department of Economics.
    3. Eldosouky, AbdelRahman & Saad, Walid & Mandayam, Narayan, 2021. "Resilient critical infrastructure: Bayesian network analysis and contract-Based optimization," Reliability Engineering and System Safety, Elsevier, vol. 205(C).

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