Testing the historic tracking of climate models

IPCC and others use in-sample correlations to confirm the ability of climate models to track the global surface temperature (GST) historically. However, a high correlation is a necessary but not sufficient condition for confirmation, because GST is nonstationary. In addition, the tracking errors must also be stationary. Cointegration tests using monthly hindcast data for GST generated by 22 climate change models over the period 1880-2010 are carried out for testing the hypothesis that these hindcasts track GST in the longer run. We show that, although GST and their hindcasts are highly correlated, they unanimously fail to be cointegrated. This means that all 22 models fail to track GST historically in the longer run, because their tracking errors are nonstationary. This juxtaposition of a high correlation and cointegration failure may be explained in terms of the phenomenon of spurious correlation, which occurs when data such as GST embody time trends.