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

Jan Beran and Norma Terrin

Journal of Time Series Analysis, 1994, vol. 15, issue 3, 269-278

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

Date: 1994
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