Gaussian pseudo-maximum likelihood estimation of fractional time series models

Details Gaussian pseudo-maximum likelihood estimation of fractional time series models Gaussian pseudo-maximum likelihood estimation of fractional time series models

2012-03-13

arxiv.org/abs/1203.2750v1

Annals of Statistics 2011, Vol. 39, No. 6, 3152-3181

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS931 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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 $\sqrt{n}$-consistent estimate.

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