COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1614 Limit Theory for Explosively Cointegrated Systems Peter C.B. Phillips and Tassos Magdalinos June 2007 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. |
