We prove in this paper the validity of an Edgeworth expansion to the joint distribution of the sample autocorrelations of a stationary, Gaussian, long memory process. The method of proof relies of Durbin's (1980\) suitably modified conditions for the validity of a multivariate Edgeworth expansion.

The ARFIMA model has become a popular approach for analyzing time series that exhibit long-range dependence. For the Gaussian case, there has been substantial advances in the area of likelihood-based inference, including development of the asymptotic properties of the maximum likelihood...

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers many types of ARFIMA models.