This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

A General Test for the Cointegrating Rank in Vector Autoregressive Models

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Ahlgren, Niklas () (Swedish School of Economics and Business Administration)
Nyblom, Jukka () (University of Joensuu)
Abstract

The article proposes a general test for the cointegrating rank in vector autoregressive models. The test is based on the eigenvalues of the companion matrix, more precisely on the sum of the real parts of those closest to one. The roots of the companion matrix are often inspected as a diagnostic tool. Here this practice is elevated to the level of a formal test. The asymptotic distribution of the test statistic is derived and tabulated by simulation. The new test is compared with the likelihood ratio test. Neither one of the tests is dominating the other over the entire parameter space. The new test safeguards the researcher against making spurious inferences on the cointegrating rank in the presence of explosive roots and of integration of higher order than one. A numerical illustration is given.

It is shown that the limiting distribution of the eigenvalues closest to one of the companion matrix is free of nuisance parameters, a useful result in its own right. When applied to a univariate autoregressive model, the augmented Dickey—Fuller test is obtained. The new test can be regarded as the multivariate version of the Dickey—Fuller coefficent test of a unit root. When there is a single common trend, the suggested test statistic has the same asymptotic distribution as the least squares estimate of the autoregressive coeficent in a univariate first order autoregressive model with a unit root. In the numerical application the test is applied to Swedish money demand data, and it is shown how to determine the cointegrating rank using the new test. The results from a small sample simulation experiment mimicking the actual data used in the application are also discussed.

Download Info
To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.

Publisher Info
Paper provided by Hanken School of Economics in its series Working Papers with number 499.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 37 pages
Date of creation: 31 Dec 2003
Date of revision:
Handle: RePEc:hhb:hanken:0499

Note: This paper is published as: Ahlgren, Niklas and Nyblom, Jukka (2008), 'Tests against Stationary and Explosive Alternatives in Vector Autoregressive Models', Journal of Time Series Analysis, 29, 421-443.
Contact details of provider:
Postal: Hanken School of Economics, Arkadiankatu 22, P.O.B. 479; FIN 00101 Helsinki, Finland
Phone: +358-9-431 331
Fax: +358-9-431 33 333
Web page: http://www.hanken.fi
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Marcus Sandberg).

Related research
Keywords: Common trends; Companion matrix; Eigenvalue test; Integration of order 2; Rank determination; Unit roots;

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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.:
  1. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June. [Downloadable!] (restricted)
    Other versions:
  2. Kirstin Hubrich & Helmut Lütkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor and Francis Journals, vol. 20(3), pages 247-318. [Downloadable!] (restricted)
    Other versions:
  3. Saikkonen, Pentti & L tkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(03), pages 373-406, June. [Downloadable!]
  4. repec:cup:etheor:v:13:y:1997:i:4:p:529-57 is not listed on IDEAS
  5. Toda, Hiro Y., 1995. "Finite Sample Performance of Likelihood Ratio Tests for Cointegrating Ranks in Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1015-1032, October. [Downloadable!]
  6. repec:cup:etheor:v:11:y:1995:i:5:p:1015-32 is not listed on IDEAS
  7. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
  8. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June. [Downloadable!] (restricted)
  9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
    Other versions:
  10. Harris, David, 1997. "Principal Components Analysis of Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 13(04), pages 529-557, August. [Downloadable!]
  11. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January. [Downloadable!] (restricted)
  12. Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 205-230. [Downloadable!] (restricted)
Full references

Statistics
Access and download statistics

Did you know? You can create a compilation of all publications of a group of people, say alumni of a program, your students or memers of an association.

This page was last updated on 2009-11-25.


This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.