Hypothesis Testing in a Fractional Ornstein-Uhlenbeck Model

Abstract EN

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.