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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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    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. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    3. Robatto, Roberto & Szentes, Balázs, 2017. "On the biological foundation of risk preferences," Journal of Economic Theory, Elsevier, vol. 172(C), pages 410-422.
    4. Li, Yingying & Zhang, Zhiyuan & Zheng, Xinghua, 2013. "Volatility inference in the presence of both endogenous time and microstructure noise," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2696-2727.
    5. Seungmoon Choi, 2011. "Closed-Form Likelihood Expansions for Multivariate Time-Inhomogeneous Diffusions," School of Economics and Public Policy Working Papers 2011-26, University of Adelaide, School of Economics and Public Policy.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Xiaowei Zhang & Peter W. Glynn, 2018. "Affine Jump-Diffusions: Stochastic Stability and Limit Theorems," Papers 1811.00122, arXiv.org.
    12. Aït-Sahalia, Yacine & Mykland, Per A., 2008. "An analysis of Hansen-Scheinkman moment estimators for discretely and randomly sampled diffusions," Journal of Econometrics, Elsevier, vol. 144(1), pages 1-26, May.
    13. 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.
    14. 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.
    15. Guay, François & Schwenkler, Gustavo, 2021. "Efficient estimation and filtering for multivariate jump–diffusions," Journal of Econometrics, Elsevier, vol. 223(1), pages 251-275.
    16. Yingying Li & Zhiyuan Zhang & Xinghua Zheng, 2013. "Volatility Inference in the Presence of Both Endogenous Time and Microstructure Noise," Papers 1303.5809, arXiv.org.
    17. 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.
    18. Hall, George & Rust, John, 2021. "Estimation of endogenously sampled time series: The case of commodity price speculation in the steel market," Journal of Econometrics, Elsevier, vol. 222(1), pages 219-243.
    19. Liron Ravner, 2022. "Queue input estimation from discrete workload observations," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 541-543, April.
    20. 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.
    21. Anne Philippe & Caroline Robet & Marie-Claude Viano, 2021. "Random discretization of stationary continuous time processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 375-400, April.
    22. 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.
    23. Liu, Zhe & Yang, Ying, 2022. "Moment estimation for parameters in high-order uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    24. Azam Asanjarani & Yoni Nazarathy & Peter Taylor, 2021. "A survey of parameter and state estimation in queues," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 39-80, February.

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