An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d satisfying 0 < d < 1/2. The theory is then applied to deliver formulae for the long run covariance matrices of multivariate time series with long memory.
Phillips, Peter C.B. and Kim, Chang Sik, "Long Run Covariance Matrices for Fractionally Integrated Processes" (2007). Cowles Foundation Discussion Papers. 1907.