A RESIDUAL-BASED LM-TYPE TEST AGAINST FRACTIONAL COINTEGRATION
提出一种检验无协整原假设的LM型检验，基于差分变量回归的残差构建统计量，具有标准正态极限分布，蒙特卡洛实验验证了有限样本性能。
Nonstationary integrated time series may be fractionally cointegrated. Here we propose a test for the null hypothesis of no cointegration. It builds on the asymptotically normal Lagrange multiplier (LM) test against fractional alternatives applied to single equation residuals. It is shown that the LM test applied naively to residuals from a static level regression does not retain asymptotic normality. However, when the LM statistic is employed with residuals from a regression of differenced variables, then the test statistic is shown to have a standard normal limiting distribution. Monte Carlo experiments establish its relevance in finite samples.We thank Norbert Christopeit and three anonymous referees for corrections and very valuable comments.