 Asymptotic normality of the principal components of functional time seriesPiotr Kokoszka and Matthew Reimherr Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1546-1562 Abstract: We establish the asymptotic normality of the sample principal components of functional stochastic processes under nonrestrictive assumptions which admit nonlinear functional time series models. We show that the aforementioned asymptotic depends only on the asymptotic normality of the sample covariance operator, and that the latter condition holds for weakly dependent functional time series which admit expansions as Bernoulli shifts. The weak dependence is quantified by the condition of L4-m-approximability which includes all functional time series models in practical use. We also demonstrate convergence of the cross covariance operators of the sample functional principal components to their counterparts in the normal limit. Keywords: Asymptotic normality; Functional principal components; Weak dependence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:5:p:1546-1562 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2012.12.011 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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