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Notes on drift estimation for certain non-recurrent diffusion processes from sampled data

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  • Shimizu, Yasutaka

Abstract

Given discrete samples from Ornstein-Uhlenbeck processes, we consider two kinds of approximated MLE's for the drift parameter, which are asymptotically efficient in ergodic case. Our interest is the rate of convergence of those estimators when the process is non-recurrent. We add a remark when the underlying process has a slightly more general drift.

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  • Shimizu, Yasutaka, 2009. "Notes on drift estimation for certain non-recurrent diffusion processes from sampled data," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2200-2207, October.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:20:p:2200-2207
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    References listed on IDEAS

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    1. Kasonga, R. A., 1988. "The consistency of a non-linear least squares estimator from diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 263-275, December.
    2. Dietz Hans M. & Kutoyants Yury A., 2003. "Parameter estimation for some non-recurrent solutions of SDE," Statistics & Risk Modeling, De Gruyter, vol. 21(1/2003), pages 29-46, January.
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    Cited by:

    1. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    2. Hui Jiang & Xing Dong, 2015. "Parameter estimation for the non-stationary Ornstein–Uhlenbeck process with linear drift," Statistical Papers, Springer, vol. 56(1), pages 257-268, February.
    3. Yasutaka Shimizu, 2012. "Local asymptotic mixed normality for discretely observed non-recurrent Ornstein–Uhlenbeck processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 193-211, February.
    4. Bercu, Bernard & Coutin, Laure & Savy, Nicolas, 2012. "Sharp large deviations for the non-stationary Ornstein–Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3393-3424.

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