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ASYMPTOTIC THEORY FOR MAXIMUM LIKELIHOOD ESTIMATION OF THE MEMORY PARAMETER IN STATIONARY GAUSSIAN PROCESSES

Published online by Cambridge University Press:  13 September 2011

Offer Lieberman ,
Roy Rosemarin  and
Judith Rousseau
Offer Lieberman*
Affiliation:
University of Haifa
Roy Rosemarin
Affiliation:
London School of Economics
Judith Rousseau
Affiliation:
CEREMADE, University Paris Dauphine
*
*Address correspondence to Offer Lieberman, Department of Economics, University of Haifa, Haifa 31905, Israel; e-mail: offerl@econ.haifa.ac.il.
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Abstract

Consistency, asymptotic normality, and efficiency of the maximum likelihood estimator for stationary Gaussian time series were shown to hold in the short memory case by Hannan (1973, Journal of Applied Probability 10, 130–145) and in the long memory case by Dahlhaus (1989, Annals of Statistics 34, 1045–1047). In this paper we extend these results to the entire stationarity region, including the case of antipersistence and noninvertibility.

Type
MISCELLANEA
Information
Econometric Theory , Volume 28 , Issue 2 , April 2012 , pp. 457 - 470
Copyright
Copyright © Cambridge University Press 2011

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