This paper considers the asymptotic distribution of the sample covariance of a nonstationary fractionally integrated process with the stationary increments of another such process—possibly itself. Questions of interest include the relationship between the harmonic representation of these...

The so-called type I and type II fractional Brownian motions are limit distributions associated with the fractional integration model in which pre-sample shocks are either included in the lag structure, or suppressed. There can be substantial differences between the distributions of these two...