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Gaussian pseudo-maximum likelihood estimation of fractional time series models

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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 asymp- totic normality) can be difficult owing to non-uniform convergence of the objective function over a large admissible parameter space. In particular, this is the case for the conditional sum of squares es- timate, 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 pn-consistent estimate. Finite sample performance of the procedure is presented by means of a Monte Carlo experiment, along with an application to real data.

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en

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http://eprints.lse.ac.uk/42013/

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