ESTIMATION OF THE LONG‐MEMORY PARAMETER, BASED ON A MULTIVARIATE CENTRAL LIMIT THEOREM

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Abstract
Long memory is known to occur in many fields of statistical application. Stationary processes whose correlations decay asymptotically like ‖k‖2H‐2, wherekis the lag andHε (0.5, 1), provide useful parsimonious models with long memory. The parameterHcharacterizes the long‐memory features of the data. For long time series, maximum likelihood estimation ofHcan be costly in terms of CPU time. In this paper, we show that, for disjoint stretches of the data, estimates ofHand other parameters that characterize the dependence structure are asymptotically independent. Averaging these estimates leads to a fast and efficient approximate maximum likelihood method.