Limit theory for explosively cointegrated systems
Limit theory for explosively cointegrated systems
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 . 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.
865-887
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31
1 August 2008
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31
Phillips, Peter Charles Bonest and Magdalinos, Tassos
(2008)
Limit theory for explosively cointegrated systems.
Econometric Theory, 24 (4), .
(doi:10.1017/S0266466608080353).
Abstract
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 . 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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e-pub ahead of print date: 4 April 2008
Published date: 1 August 2008
Identifiers
Local EPrints ID: 472214
URI: http://eprints.soton.ac.uk/id/eprint/472214
ISSN: 0266-4666
PURE UUID: 6299253c-e3cb-4ffb-9258-1de10d1e24b5
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Date deposited: 29 Nov 2022 17:49
Last modified: 16 Mar 2024 22:40
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