AMS 1980 subject classification: 62G10, 62M10.
long memory process
local asymptotic normality
locally asymptotically minimax estimator
Springer Online Journal Archives 1860-2000
Abstract Various estimators of the lag parameter of long–memory processes have been proposed in the literature. Such estimators, at best, are asymptotically efficient (in the traditional BAN sense) under Gaussian assumptions. An adaptive estimate, which is uniformly (with respect to the underlying innovation density) locally asymptotically minimax (LAM) in the sense of Fabian and Hannan (1982), is proposed here for the lag parameter d in the simple long–memory model (1−L)d Xt=εt.
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