Cointegration Analysis of Commodity Prices: Much Ado about the Wrong Thing?

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.