This study highlights some problems with using the Johansen cointegration statistics on data containing a negative moving average (NMA) in the error term of the data generating process. We use a Monte Carlo experiment to demonstrate that the asymptotic distribution of the Johansen cointegration statistics is sensitive to the NMA parameters and that using the stated 5% critical values results in severe size distortion. In our experiment, using the asymptotic critical values resulted in empirical size of 76% in the worst case. To date a NMA in the error term was known to cause poor small sample performance of the Johansen cointegration statistics; however our study demonstrates that problems associated with a NMA in the error term do not improve as sample size increases. In fact, the problems become more severe. Further, we show that commodity prices in the U.S. tend to exhibit this property. We recommend that researchers pretest data for NMA in the error term before using the standard asymptotic critical values to test for cointegrating rank.

我们使用蒙特卡洛实验来证明Johansen协整统计量的渐近分布对NMA参数是敏感的，并且使用规定的5%临界值会导致严重的尺寸畸变。在我们的实验中，使用渐近临界值在最坏情况下得到了76%的经验大小。到目前为止，在误差项中的NMA已知会导致Johansen协整统计量的小样本性能不佳;然而，我们的研究表明，与误差项相关的NMA问题不会随着样本量的增加而改善。事实上，问题变得更加严重。此外，我们表明，美国的商品价格往往表现出这种特性。我们建议研究人员在使用标准渐近临界值来检验协整秩之前，在误差项中预先检验NMA数据。