Sample autocorrelations of nonstationary fractionally integrated series

We derive the asymptotic distribution of the sample autocorrelations of nonstationary fractionally integrated processes of order d. If d greater than or equal to 1, the sample autocorrelations approach their probability limit one with a rate equal to the sample size. If d<1, the rate is slower and depends on d. These findings carry over to the case of detrended series. Monte Carlo evidence and an empirical example illustrate the theoretical results.