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 Q are
distinct, the centered least squares estimator has an exponential Qn 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 Mn+ 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+
