IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Robust parameter estimation for the Ornstein–Uhlenbeck process

  • Sonja Rieder

    ()

Registered author(s):

    In this paper, we derive elementary M- and optimally robust asymptotic linear (AL)-estimates for the parameters of an Ornstein–Uhlenbeck process. Simulation and estimation of the process are already well-studied, see Iacus (Simulation and inference for stochastic differential equations. Springer, New York, 2008 ). However, in order to protect against outliers and deviations from the ideal law the formulation of suitable neighborhood models and a corresponding robustification of the estimators are necessary. As a measure of robustness, we consider the maximum asymptotic mean square error (maxasyMSE), which is determined by the influence curve (IC) of AL estimates. The IC represents the standardized influence of an individual observation on the estimator given the past. In a first step, we extend the method of M-estimation from Huber (Robust statistics. Wiley, New York, 1981 ). In a second step, we apply the general theory based on local asymptotic normality, AL estimates, and shrinking neighborhoods due to Kohl et al. (Stat Methods Appl 19:333–354, 2010 ), Rieder (Robust asymptotic statistics. Springer, New York, 1994 ), Rieder ( 2003 ), and Staab ( 1984 ). This leads to optimally robust ICs whose graph exhibits surprising behavior. In the end, we discuss the estimator construction, i.e. the problem of constructing an estimator from the family of optimal ICs. Therefore we carry out in our context the One-Step construction dating back to LeCam (Asymptotic methods in statistical decision theory. Springer, New York, 1969 ) and compare it by means of simulations with MLE and M-estimator. Copyright Springer-Verlag 2012

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://hdl.handle.net/10.1007/s10260-012-0195-2
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Springer in its journal Statistical Methods & Applications.

    Volume (Year): 21 (2012)
    Issue (Month): 4 (November)
    Pages: 411-436

    as
    in new window

    Handle: RePEc:spr:stmapp:v:21:y:2012:i:4:p:411-436
    Contact details of provider: Web page: http://link.springer.de/link/service/journals/10260/index.htm

    Order Information: Web: http://link.springer.de/orders.htm

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Loriano Mancini & Elvezio Ronchetti & Fabio Trojani, 2005. "Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models," University of St. Gallen Department of Economics working paper series 2005 2005-01, Department of Economics, University of St. Gallen.
    2. Yuji Sakamoto & Nakahiro Yoshida, 1998. "Asymptotic Expansion of M ‐Estimator Over Wiener Space," Statistical Inference for Stochastic Processes, Springer, vol. 1(1), pages 85-103, January.
    3. Croux, C. & Dehon, C., 2010. "Influence Functions of the Spearman and Kendall Correlation Measures," Discussion Paper 2010-40, Tilburg University, Center for Economic Research.
    4. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer, vol. 42(2), pages 221-251, June.
    5. Matthias Kohl & Peter Ruckdeschel & Helmut Rieder, 2010. "Infinitesimally Robust estimation in general smoothly parametrized models," Statistical Methods and Applications, Springer, vol. 19(3), pages 333-354, August.
    6. Marc Hallin & Christophe Koell & Bas Werker, 2000. "Optimal inference for discretely observed semiparametric Ornstein-Uhlenbeck processes," ULB Institutional Repository 2013/2097, ULB -- Universite Libre de Bruxelles.
    7. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    8. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods and Applications, Springer, vol. 19(4), pages 497-515, November.
    9. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    10. Swensen, Anders Rygh, 1985. "The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 54-70, February.
    11. Tadeusz Bednarski, 2010. "Fréchet differentiability in statistical inference for time series," Statistical Methods and Applications, Springer, vol. 19(4), pages 517-528, November.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:spr:stmapp:v:21:y:2012:i:4:p:411-436. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)

    or (Christopher F Baum)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.