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Estimation of Continuous-Time Markov Processes Sampled at Random Time Intervals

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  • Darrell Duffie
  • Peter Glynn

Abstract

We introduce a family of generalized-method-of-moments estimators of the parameters of a continuous-time Markov process observed at random time intervals. The results include strong consistency, asymptotic normality, and a characterization of standard errors. Sampling is at an arrival intensity that is allowed to depend on the underlying Markov process and on the parameter vector to be estimated. We focus on financial applications, including tick-based sampling, allowing for jump diffusions, regime-switching diffusions, and reflected diffusions. Copyright The Econometric Society 2004.

Suggested Citation

  • Darrell Duffie & Peter Glynn, 2004. "Estimation of Continuous-Time Markov Processes Sampled at Random Time Intervals," Econometrica, Econometric Society, vol. 72(6), pages 1773-1808, November.
  • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:6:p:1773-1808
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00553.x
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    Citations

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    Cited by:

    1. Chen, Xiaohong & Hansen, Lars Peter & Carrasco, Marine, 2010. "Nonlinearity and temporal dependence," Journal of Econometrics, Elsevier, vol. 155(2), pages 155-169, April.
    2. repec:kap:compec:v:51:y:2018:i:2:d:10.1007_s10614-017-9692-6 is not listed on IDEAS
    3. repec:eee:jetheo:v:172:y:2017:i:c:p:410-422 is not listed on IDEAS
    4. Mor Armony & Erica L. Plambeck, 2005. "The Impact of Duplicate Orders on Demand Estimation and Capacity Investment," Management Science, INFORMS, vol. 51(10), pages 1505-1518, October.
    5. Renault, Eric & Werker, Bas J.M., 2011. "Causality effects in return volatility measures with random times," Journal of Econometrics, Elsevier, vol. 160(1), pages 272-279, January.
    6. repec:wsi:apjorx:v:34:y:2017:i:01:n:s0217595917400097 is not listed on IDEAS
    7. I. Gaia Becheri & Feike C. Drost & Bas J.M. Werker, 2016. "Asymptotic Inference for Jump Diffusions with State-Dependent Intensity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 520-542, June.
    8. Bandi, Federico M. & Phillips, Peter C.B., 2007. "A simple approach to the parametric estimation of potentially nonstationary diffusions," Journal of Econometrics, Elsevier, vol. 137(2), pages 354-395, April.
    9. Pastorello, S. & Rossi, E., 2010. "Efficient importance sampling maximum likelihood estimation of stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2753-2762, November.
    10. Yu, Jialin, 2007. "Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan," Journal of Econometrics, Elsevier, vol. 141(2), pages 1245-1280, December.

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