The Fractional Unit Root Distribution

Abstract

Asymptotic distributions are derived for the ordinary least squares estimate of a first order autoregression model when the series is fractionally integrated. The fractional unit root distribution is introduced to describe the limiting distribution. The unit root distribution is shown to be an atypical member of this family because its density is nonzero over the entire real line. For -1/2 Copyright 1990 by The Econometric Society.