Limit Theory for Explosively Cointegrated Systems
AbstractA limit theory is developed for multivariate regression in an explosive cointegrated system. The asymptotic behavior of the least squares estimator of the cointegrating coefficients is found to depend upon the precise relationship between the explosive regressors. When the eigenvalues of the autoregressive matrix are distinct, the centered least squares estimator has an exponential rate of convergence and a mixed normal limit distribution. No central limit theory is applicable here and Gaussian innovations are assumed. On the other hand, when some regressors exhibit common explosive behavior, a different mixed normal limiting distribution is derived with rate of convergence reduced to n^0.5. In the latter case, mixed normality applies without any distributional assumptions on the innovation errors by virtue of a Lindeberg type central limit theorem. Conventional statistical inference procedures are valid in this case, the stationary convergence rate dominating the behavior of the least squares estimator.
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 1614.
Length: 24 pages
Date of creation: Jun 2007
Date of revision:
Publication status: Published in Econometric Theory (August 2008), 24(4): 865-887
Note: CFP 1244
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:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-06-23 (All new papers)
- NEP-ECM-2007-06-23 (Econometrics)
- NEP-ETS-2007-06-23 (Econometric Time Series)
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Peter C.B. Phillips & Tassos Magdalinos, 2011.
"Inconsistent VAR Regression with Common Explosive Roots,"
Cowles Foundation Discussion Papers
1777, Cowles Foundation for Research in Economics, Yale University.
- Phillips, Peter C.B. & Magdalinos, Tassos, 2013. "Inconsistent Var Regression With Common Explosive Roots," Econometric Theory, Cambridge University Press, vol. 29(04), pages 808-837, August.
- Peter C.B. Phillips & Ji Hyung Lee, 2012. "VARs with Mixed Roots Near Unity," Cowles Foundation Discussion Papers 1845, Cowles Foundation for Research in Economics, Yale University.
- Peter C.B. Phillips & Tassos Magdalinos, 2008.
"Unit Root and Cointegrating Limit Theory When Initialization Is in the Infinite Past,"
Cowles Foundation Discussion Papers
1655, Cowles Foundation for Research in Economics, Yale University.
- Phillips, Peter C.B. & Magdalinos, Tassos, 2009. "Unit Root And Cointegrating Limit Theory When Initialization Is In The Infinite Past," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1682-1715, December.
- B. Nielsen, 2009. "Test for cointegration rank in general vector autoregressions," Economics Papers 2009-W10, Economics Group, Nuffield College, University of Oxford.
- Peter C.B. Phillips & Sainan Jin, 2013. "Testing the Martingale Hypothesis," Cowles Foundation Discussion Papers 1912, Cowles Foundation for Research in Economics, Yale University.
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.