Hypothesis Testing in a Fractional Ornstein-Uhlenbeck Model

Michael Moers

International Journal of Stochastic Analysis, 2012, vol. 2012, 1-23

Abstract:

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:268568

DOI: 10.1155/2012/268568

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