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Asymptotic Theory for Maximum Likelihood Estimation of the Memory Parameter in Stationary Gaussian Processes

Lieberman, Offer; Rosemarin, Roy; Rousseau, Judith (2012), Asymptotic Theory for Maximum Likelihood Estimation of the Memory Parameter in Stationary Gaussian Processes, Econometric Theory, 28, 2, p. 457-470. http://dx.doi.org/10.1017/S0266466611000399

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00641474/fr/
Date
2012
Journal name
Econometric Theory
Volume
28
Number
2
Publisher
Cambridge University Press
Pages
457-470
Publication identifier
Metadata
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Author(s)
Lieberman, Offer
Rosemarin, Roy
Rousseau, Judith
Abstract (EN)
Consistency, asymptotic normality and e ciency of the maximum likelihood estimator for stationary Gaussian time series, were shown to hold in the short memory case by Hannan (1973) and in the long memory case by Dahlhaus (1989). In this paper, we extend these results to the entire stationarity region, including the case of intermediate memory and noninvertibility. In the process of proving the main results, we provide a useful theorem on the limiting behavior of a product of Toeplitz matrices under strictly weaker conditions than those employed by Dahlhaus (1989).
Subjects / Keywords
Intermediate Memory; Long Range Dependence; Maximum Likelihood Estimation; Toeplitz Matrix
JEL
C13 - Estimation: General
C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes