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.
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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
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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 &bull Diffusion Processes
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)
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- Phillips, Peter C.B. & Magdalinos, Tassos, 2013.
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Cowles Foundation Discussion Papers
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