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 central limit theorem in Davidson [2] is extended to allow cases where the variances of sequence coordinates can be tending to zero. A trade-off is demonstrated between the degree of dependence and the rate of degeneration. For the martingale difference case, it is sufficient for the sum of...

We consider the Breitung (2002, <italic>Journal of Econometrics</italic> 108, 343–363) statistic ξ_null, which provides a nonparametric test of the I(1) hypothesis. If ξ denotes the limit in distribution of ξ_null as <italic>n</italic> → ∞, we prove (Theorem 1) that 0 ≤ ξ ≤ 1/π², a result that holds under any...

A central limit theorem is proved for dependent stochastic processes. Global heterogeneity of the distribution of the terms is permitted, including asymptotically unbounded moments. The approach is to adapt a CLT for martingale differences due to McLeish and show that suitably defined Bernstein...