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International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 268568, 23 pages
Research Article

Hypothesis Testing in a Fractional Ornstein-Uhlenbeck Model

Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA

Received 31 May 2012; Accepted 2 October 2012

Academic Editor: Qing Zhang

Copyright © 2012 Michael Moers. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Consider an Ornstein-Uhlenbeck process driven by a fractional Brownian motion. It is an interesting problem to find criteria for whether the process is stable or has a unit root, given a finite sample of observations. Recently, various asymptotic distributions for estimators of the drift parameter have been developed. We illustrate through computer simulations and through a Stein's bound that these asymptotic distributions are inadequate approximations of the finite-sample distribution for moderate values of the drift and the sample size. We propose a new model to obtain asymptotic distributions near zero and compute the limiting distribution. We show applications to regression analysis and obtain hypothesis tests and their asymptotic power.