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


  • Darrell Duffie
  • Peter Glynn


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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    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. Robatto, Roberto & Szentes, Balázs, 2017. "On the biological foundation of risk preferences," Journal of Economic Theory, Elsevier, vol. 172(C), pages 410-422.
    3. 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.
    4. Shuang Xiao & Guo Li & Yunjing Jia, 2017. "Estimating the Constant Elasticity of Variance Model with Data-Driven Markov Chain Monte Carlo Methods," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-23, February.
    5. 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.
    6. 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.
    7. 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.
    8. Xiaowei Zhang & Peter W. Glynn, 2018. "Affine Jump-Diffusions: Stochastic Stability and Limit Theorems," Papers 1811.00122,
    9. 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.
    10. Yogo Purwono & Irwan Adi Ekaputra & Zaäfri Ananto Husodo, 2018. "Estimation of Dynamic Mixed Hitting Time Model Using Characteristic Function Based Moments," Computational Economics, Springer;Society for Computational Economics, vol. 51(2), pages 295-321, February.
    11. 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.
    12. Erik Lindström, 2007. "Estimating parameters in diffusion processes using an approximate maximum likelihood approach," Annals of Operations Research, Springer, vol. 151(1), pages 269-288, April.
    13. Anne Philippe & Caroline Robet & Marie-Claude Viano, 0. "Random discretization of stationary continuous time processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 0, pages 1-26.
    14. Yiying Cheng & Yaozhong Hu & Hongwei Long, 2020. "Generalized moment estimators for $$\alpha $$α-stable Ornstein–Uhlenbeck motions from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 53-81, April.

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