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ESTIMATION OF THE LONG‐MEMORY PARAMETER, BASED ON A MULTIVARIATE CENTRAL LIMIT THEOREM
Author(s) -
Beran Jan,
Terrin Norma
Publication year - 1994
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1994.tb00192.x
Subject(s) - mathematics , central limit theorem , disjoint sets , multivariate statistics , series (stratigraphy) , limit (mathematics) , long memory , estimation theory , maximum likelihood , statistics , statistical physics , econometrics , combinatorics , mathematical analysis , volatility (finance) , paleontology , physics , biology
. Long memory is known to occur in many fields of statistical application. Stationary processes whose correlations decay asymptotically like ‖ k ‖ 2 H ‐2 , where k is the lag and H ε (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.