LIMIT THEORY FOR EXPLOSIVELY COINTEGRATED SYSTEMS
研究了爆炸性协整系统中多元回归的极限理论，发现协整系数最小二乘估计量的渐近行为取决于爆炸性回归变量之间的关系，不同情况下收敛速度和极限分布不同。
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 Θ n 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 $\sqrt{n}$ . 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.