Asymptotic Properties of Residual Based Tests for Cointegration
AbstractThis paper develops an asymptotic theory for residual based tests for cointegration. These tests involve procedures that are designed to detect the presence of a unit root in the residuals of (cointegrating) regressions among the levels of economic time series. Attention is given to the augmented Dickey-Fuller (ADF) test that is recommended by Engle-Granger (1987) and the Z(a) and Z(t) unit root tests recently proposed by Phillips (1987). Two new tests are also introduced, one of which is invariant to the normalization of the cointegrating regression. All of these tests are shown to be asymptotically similar and simple representations of their limiting distributions are given in terms of standard Brownian motion. The ADF and Z(t) tests are asymptotically equivalent. Power properties of the tests are also studied. The analysis shows that all the tests are consistent if suitably constructed but that the ADF and Z(t) tests have slower rates of divergence under cointegration than the other tests. This indicates that, at least in large samples, the Z(a) test should have superior power properties.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. 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.
Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 847R.
Length: 51 pages
Date of creation: 1987
Date of revision: Jul 1988
Publication status: Published in Econometrica (January 1990), 58(1): 165-193
Note: CFP 746.
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Other versions of this item:
- Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).
If references are entirely missing, you can add them using this form.