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On maximum likelihood estimation of the drift matrix of a degenerated O–U process

Author

Listed:
  • Ana Prior

    (Instituto Politécnico de Lisboa)

  • Marina Kleptsyna

    (Université du Maine)

  • Paula Milheiro-Oliveira

    (Universidade do Porto)

Abstract

In this work, we consider a 2n-dimension Ornstein–Uhlenbeck (O–U) process with a singular diffusion matrix. This process represents a currently used model for mechanical systems subject to random vibrations. We study the problem of estimating the drift parameters of the stochastic differential equation that governs the O–U process. The maximum likelihood estimator proposed and explored in Koncz (J Anal Math 13(1):75–91, 1987) is revisited and applied to our model. We prove the local asymptotic normality property and the convergence of moments of the estimator. Simulation studies based on representative examples taken from the literature illustrate the obtained theoretical results.

Suggested Citation

  • Ana Prior & Marina Kleptsyna & Paula Milheiro-Oliveira, 2017. "On maximum likelihood estimation of the drift matrix of a degenerated O–U process," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 57-78, April.
    • Handle: RePEc:spr:sistpr:v:20:y:2017:i:1:d:10.1007_s11203-016-9137-1
    DOI: 10.1007/s11203-016-9137-1
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    References listed on IDEAS

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    1. Samson, Adeline & Thieullen, Michèle, 2012. "A contrast estimator for completely or partially observed hypoelliptic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2521-2552.
    2. N. Lin & S. Lototsky, 2014. "Second-order continuous-time non-stationary Gaussian autoregression," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 19-49, April.
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