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Estimating the transition matrix of a Markov chain observed at random times

Author

Listed:
  • Barsotti, Flavia
  • De Castro, Yohann
  • Espinasse, Thibault
  • Rochet, Paul

Abstract

We want to recover the transition kernel P of a Markov chain X when only a sub-sequence of X is available. The time gaps between the observations are iid with unknown distribution. We propose a method to build an estimator of P under the assumption that it has some zero entries. Its asymptotic performance is discussed in theory and through numerical simulations.

Suggested Citation

  • Barsotti, Flavia & De Castro, Yohann & Espinasse, Thibault & Rochet, Paul, 2014. "Estimating the transition matrix of a Markov chain observed at random times," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 98-105.
    • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:98-105
    DOI: 10.1016/j.spl.2014.07.009
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    References listed on IDEAS

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    1. Pittenger, A. O., 1982. "Time changes of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 13(2), pages 189-199, August.
    2. MacRae, Elizabeth Chase, 1977. "Estimation of Time-Varying Markov Processes with Aggregate Data," Econometrica, Econometric Society, vol. 45(1), pages 183-198, January.
    3. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    4. Robert B. Israel & Jeffrey S. Rosenthal & Jason Z. Wei, 2001. "Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit Ratings," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 245-265, April.
    5. Bruce A. Craig & Peter P. Sendi, 2002. "Estimation of the transition matrix of a discrete‐time Markov chain," Health Economics, John Wiley & Sons, Ltd., vol. 11(1), pages 33-42, January.
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