GAUSSIAN PSEUDO-MAXIMUM LIKELIHOOD ESTIMATION OF FRACTIONAL TIME SERIES MODELS

• 成果类型: Article
• 署名作者: Hualde, Javier; Robinson, Peter M.
• 署名单位: Universidad Publica de Navarra; University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS931
• 发表日期: 2011
• 页码: 3152-3181
• 关键词: long-range dependence; stationary; parameter; integration; inference

摘要

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 non-invertible 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 root n-consistent estimate.