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LIMIT THEORY FOR EXPLOSIVELY COINTEGRATED SYSTEMS

Published online by Cambridge University Press:  04 April 2008

Peter C.B. Phillips  and
Tassos Magdalinos
Peter C.B. Phillips*
Affiliation:
Cowles Foundation for Research in Economics, Yale University, University of Auckland and University of York
Tassos Magdalinos
Affiliation:
University of Nottingham
*
Address correspondence to Peter C.B. Phillips, Department of Economics, Yale University, P.O. Box 208268, New Haven, CT 06520-8268, USA; e-mail: peter.phillips@yale.edu.
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Abstract

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A 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 Θ are distinct, the centered least squares estimator has an exponential Θn 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 $\sqrt{n}$ . 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.

Information

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 865 - 887
Copyright
Copyright © Cambridge University Press 2008

References

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