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Discussion Paper

Valid Edgeworth Expansions for the Whittle Maximum Likelihood Estimator for Stationary Long-memory Gaussian Time Series

In this paper, we prove the validity of an Edgeworth expansion to the distribution of the Whittle maximum likelihood estimator for stationary long-memory Gaussian models with unknown parameter . The error of the (s-2)-order expansion is shown to be o(n(s-2)/2) – the usual iid rate — for a wide range of models, including the popular ARFIMA(p,d,q) models.