Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes

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Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes

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Title: Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes
Author: Davidson, James
Citation: Journal of Econometrics 106 (2002) 243-269
Publisher: Elsevier
Journal: Journal of Econometrics
Date Issued: 2002
URI: http://hdl.handle.net/10036/28753
DOI: 10.1016/S0304-4076(01)00100-2
Links: http://www.people.ex.ac.uk/jehd201/ http://www.sciencedirect.com/science/journal/03044076
Abstract: This paper considers methods of deriving sufficient conditions for the central limit theorem and functional central limit theorem to hold in a broad class of time series processes, including nonlinear processes and semiparametric linear processes. The common thread linking these results is the concept of near-epoch dependence on a mixing process, since powerful limit results are available under this limited-dependence property. The particular case of near-epoch dependence on an independent process provides a convenient framework for dealing with a range of nonlinear cases, including the bilinear, GARCH, and threshold autoregressive models. It is shown in particular that even SETAR processes with a unit root regime have short memory, under the right conditions. A simulation approach is also demonstrated, applicable to cases that are analytically intractable. A new FCLT is given for semiparametric linear processes, where the forcing processes are of the NED-on-mixing type, under conditions that are evidently close to necessary.
Type: Article
Description: Please see also the following Corrigendum to Section 2.4, Journal of Econometrics 110(1) 103-104The author was formerly at the Cardiff Business School
Keywords: near epoch dependenceGARCHFCLTTARNonlinearBilinear
ISSN: 03044076


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