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Parameter estimation for a discrete sampling of an integrated Ornstein-Uhlenbeck process

Abstract : We study the estimation of parameters theta = (mu, sigma (2)) for a diffusion dX(t) = a(X-t, sigma (2))dB(t) + b(X-t, mu )dt, when we observe a discretization with step Delta of the integral I-t = integral (t)(0)X(s)ds. To keep computations tractable we focus on the case of an Ornstein-Uhlenbeck process, but our results provide information on how to deal with other processes. We study an efficient estimator <()over cap>(n) based on the Gaussian property of the process (integral ((i+1)Delta)(i Delta)X(s)ds)(i greater than or equal to0), and we give an estimator <()over bar>(n) based on Ryden's idea of maximum likelihood split data. We compare these different estimators: first we give some numerical results, then we give a theoretical explanation for these results.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693749
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Submitted on : Wednesday, May 2, 2012 - 11:16:54 PM
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Arnaud Gloter. Parameter estimation for a discrete sampling of an integrated Ornstein-Uhlenbeck process. Statistics, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2001, 35 (3), pp.225--243. ⟨10.1080/02331880108802733⟩. ⟨hal-00693749⟩

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