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Limit Theory For Explosively Cointegrated Systems

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  • Phillips, Peter C.B.
  • Magdalinos, Tassos

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 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 Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 24 (2008)
Issue (Month): 04 (August)
Pages: 865-887

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Handle: RePEc:cup:etheor:v:24:y:2008:i:04:p:865-887_08

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Cited by:
  1. Xiaohu Wang & Jun Yu, 2013. "Limit Theory for an Explosive Autoregressive Process," Working Papers 08-2013, Singapore Management University, School of Economics.
  2. 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.
  3. 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.
  4. Peter C.B. Phillips & Sainan Jin, 2013. "Testing the Martingale Hypothesis," Cowles Foundation Discussion Papers 1912, Cowles Foundation for Research in Economics, Yale University.
  5. B. Nielsen, 2009. "Test for cointegration rank in general vector autoregressions," Economics Papers 2009-W10, Economics Group, Nuffield College, University of Oxford.
  6. 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.
  7. Bent Nielsen, 2008. "Singular vector autoregressions with deterministic terms: Strong consistency and lag order determination," Economics Series Working Papers 2008-W14, University of Oxford, Department of Economics.

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