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Gaussian pseudo-maximum likelihood estimation of fractional time series models

Hualde, Javier and Robinson, Peter (2011) Gaussian pseudo-maximum likelihood estimation of fractional time series models. Annals of Statistics, 39 (6). pp. 3152-3181. ISSN 0090-5364

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Identification Number: 10.1214/11-AOS931SUPP


We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible regions. In these circumstances, a proof of consistency (which is a prerequisite for proving asymptotic normality) can be difficult owing to nonuniform convergence of the objective function over a large admissible parameter space. In particular, this is the case for the conditional sum of squares estimate, which can be expected to be asymptotically efficient under Gaussianity. Without the latter assumption, we establish consistency and asymptotic normality for this estimate in case of a quite general univariate model. For a multivariate model, we establish asymptotic normality of a one-step estimate based on an initial √n-consistent estimate.

Item Type: Article
Official URL:
Additional Information: © 2012 Institute of Mathematical Statistics
Divisions: Economics
Subjects: H Social Sciences > HA Statistics
JEL classification: C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C22 - Time-Series Models
Date Deposited: 23 Feb 2012 14:16
Last Modified: 20 Jul 2021 02:10

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