An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d satisfying 0 lt; d lt; 1/2. The theory is then applied to deliver formulae for the long run covariance matrices of multivariate time series with long memory

Estimation of the memory parameter (d) is considered for models of nonstationary fractionally integrated time series with d gt; (1/2). It is shown that the log periodogram regression estimator of d is inconsistent when 1 lt; d lt; 2 and is consistent when (1/2) lt; d = 1. For d gt; 1, the...