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 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+