Infinite order vector autoregressive (VAR) models have been used in a number of applications ranging from spectral density estimation, impulse response analysis, and tests for cointegration and unit roots, to forecasting. For estimation of such models it is necessary to approximate the infinite order lag structure by finite order VARs. In practice, the order of approximation is often selected by information criteria or by general-to-specific specification tests. Unlike in the finite order VAR case these selection rules are not consistent in the usual sense, and the asymptotic properties of parameter estimates of the infinite order VAR do not follow as easily as in the finite order case. In this paper it is shown that the parameter estimates of the infinite order VAR are asymptotically normal with zero mean when the model is approximated by a finite order VAR with a data dependent lag length. The requirement for the result to hold is that the selected lag length satisfies certain rate conditions with probability tending to one. Two examples of selection rules satisfying these requirements are discussed. Uniform rates of convergence for the parameters of the infinite order VAR are also established.Very helpful comments by the editor and two referees led to a substantial improvement of the manuscript. I am particularly indebted to one of the referees for pointing out an error in the proofs. All remaining errors are my own. Financial support from NSF grant SES 0095132 is gratefully acknowledged.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 21 (2005) Issue (Month): 01 (February) Pages: 85-115 Download reference. The following formats are available: HTML
(with abstract),
plain text
(with abstract),
BibTeX,
RIS (EndNote, RefMan, ProCite),
ReDIF
Contact details of provider: Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK Fax: +44 (0)1223 325150 Email: Web page: http://journals.cambridge.org/jid_ECT
For technical questions regarding this item, or to correct its listing, contact: (Mike Eden).
Related research
Keywords:
Other versions of this item:
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)