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Unified asymptotic theory for nearly unstable AR(p) processes

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dc.contributor.authorBuchmann, Boris
dc.contributor.authorChan, Ngai Hang
dc.date.accessioned2015-12-10T23:35:11Z
dc.date.issued2013
dc.date.updated2016-02-24T08:54:14Z
dc.description.abstractA unified asymptotic theory for nearly unstable higher order autoregressive processes and their least squares estimates is established. A novel version of Jordan's canonical decomposition with perturbations together with a suitable plug-in principle is proposed to develop the underlying theories. Assumptions are stated in terms of the domain of attraction of partial Fourier transforms. The machinery is applied to recapture some of the classical results with the driving noise being martingale differences. Further, we show how to extend the results to higher order fractional ARIMA models in nearly unstable settings, thereby offering a comprehensive theory to analyse nearly unstable time series.
dc.identifier.issn0304-4149
dc.identifier.urihttp://hdl.handle.net/1885/69747
dc.publisherElsevier
dc.sourceStochastic Processes and their Applications
dc.subjectKeywords: Auto regressive models; Fractional brownian motion; Jordan canonical form; Least Square; Unit root; Fourier transforms; Machinery; Asymptotic analysis Fractional Brownian motion; Jordan canonical form; Lévy area; Least squares; Nearly unstable autoregressive model; Unit root test
dc.titleUnified asymptotic theory for nearly unstable AR(p) processes
dc.typeJournal article
local.bibliographicCitation.issue3
local.bibliographicCitation.lastpage985
local.bibliographicCitation.startpage952
local.contributor.affiliationBuchmann, Boris, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationChan, Ngai Hang, Chinese University of Hong Kong
local.contributor.authoruidBuchmann, Boris, u4164354
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.identifier.absfor010406 - Stochastic Analysis and Modelling
local.identifier.ariespublicationf5625xPUB2109
local.identifier.citationvolume123
local.identifier.doi10.1016/j.spa.2012.09.014
local.identifier.scopusID2-s2.0-84871227208
local.identifier.thomsonID000315310900010
local.type.statusPublished Version

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