Hypothesis Testing in a Fractional Ornstein-Uhlenbeck Model

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 formoderate values of the drift and the sample size.We propose a newmodel 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.