Gaussian pseudo-maximum likelihood estimation of fractional time series models

Abstract

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.

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

References in corpus (4)

• Gaussian pseudo-maximum likelihood estimation of fractional time series models
• A frequency domain empirical likelihood for short- and long-range dependence
• Efficiency improvements in inference on stationary and nonstationary fractional time series
• Conditional-sum-of-squares estimation of models for stationary time series with long memory

Cited by in corpus (5)

• Gaussian pseudo-maximum likelihood estimation of fractional time series models
• Moment bounds and mean squared prediction errors of long-memory time series
• Nonparametric Bayesian estimation of a Hölder continuous diffusion coefficient
• The modified conditional sum-of-squares estimator for fractionally integrated models
• Testing for unit roots based on sample autocovariances