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Parameter estimation of Ornstein–Uhlenbeck process generating a stochastic graph

Author

Listed:
  • Emmanuel Gobet

    (Université Paris Saclay)

  • Gustaw Matulewicz

    (Université Paris Saclay)

Abstract

Given Y a graph process defined by an incomplete information observation of a multivariate Ornstein–Uhlenbeck process X, we investigate whether we can estimate the parameters of X. We define two statistics of Y. We prove convergence properties and show how these can be used for parameter inference. Finally, numerical tests illustrate our results and indicate possible extensions and applications.

Suggested Citation

  • Emmanuel Gobet & Gustaw Matulewicz, 2017. "Parameter estimation of Ornstein–Uhlenbeck process generating a stochastic graph," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 211-235, July.
    • Handle: RePEc:spr:sistpr:v:20:y:2017:i:2:d:10.1007_s11203-016-9142-4
    DOI: 10.1007/s11203-016-9142-4
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    References listed on IDEAS

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    1. Florens-Zmirou, D., 1991. "Statistics on crossings of discretized diffusions and local time," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 139-151, October.
    2. Iacus, Stefano Maria & Uchida, Masayuki & Yoshida, Nakahiro, 2009. "Parametric estimation for partially hidden diffusion processes sampled at discrete times," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1580-1600, May.
    3. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    4. van Zanten, Harry, 2000. "A multivariate central limit theorem for continuous local martingales," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 229-235, November.
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    Cited by:

    1. Kou Fujimori, 2019. "The Dantzig selector for a linear model of diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 475-498, October.

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