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December 2011 Gaussian pseudo-maximum likelihood estimation of fractional time series models
Javier Hualde, Peter M. Robinson
Ann. Statist. 39(6): 3152-3181 (December 2011). DOI: 10.1214/11-AOS931


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.


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Javier Hualde. Peter M. Robinson. "Gaussian pseudo-maximum likelihood estimation of fractional time series models." Ann. Statist. 39 (6) 3152 - 3181, December 2011.


Published: December 2011
First available in Project Euclid: 5 March 2012

zbMATH: 1246.62186
MathSciNet: MR3012404
Digital Object Identifier: 10.1214/11-AOS931

Primary: 62F12 , 62M10

Keywords: asymptotic normality , consistency , fractional processes , Gaussian estimation , multiple time series , noninvertibility , nonstationarity

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 6 • December 2011
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