Cointegration has been mentioned previously and is one of the highest ranking search terms on landshape.
Here is the abstract.
Polynomial cointegration tests of anthropogenic impact on global warming M. Beenstock, Y. Reingewertz, and N. Paldor
Abstract. We use statistical methods for nonstationary time series to test the anthropogenic interpretation of global warming (AGW), according to which an increase in atmospheric greenhouse gas concentrations raised global temperature in the 20th century. Specifically, the methodology of polynomial cointegration is used to test AGW since during the observation period (1880–2007) global temperature and solar irradiance are stationary in 1st differences whereas greenhouse gases and aerosol forcings are stationary in 2nd differences. We show that although these anthropogenic forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance. Therefore, greenhouse gas forcing, aerosols, solar irradiance and global temperature are not polynomially cointegrated. This implies that recent global warming is not statistically significantly related to anthropogenic forcing. On the other hand, we find that greenhouse gas forcing might have had a temporary effect on global temperature.
The bottom line:
Once the I(2) status of anthopogenic forcings is taken into consideration, there is no significant effect of anthropogenic forcing on global temperature.
They do, however, find a possible effect of the CO2 first difference:
The ADF and PP test statistics suggest that there is a causal effect of the change in CO2 forcing on global temperature.
They suggest “… there is no physical theory for this modified theory of AGW”, although I would think the obvious one would be that the surface temperature adjusts over time to higher CO2 forcing, such as through intensified heat loss by convection, so returning to an equilibrium. However, when revised solar data is used the relationship disappears, so the point is probably moot.
When we use these revised data, Eqs. (11) and (12) remain polynomially uncointegrated. However, Eq. (15) ceases to be cointegrated.
For physical reasons it might be expected that over the millennia these variables should share the same order of integration; they should all be I(1) or all I(2), otherwise there would be persistent energy imbalance. However, during 150 yr there is no physical reason why these variables should share the same order of integration. However, the fact that they do not share the same order of integration over this period means that scientists who make strong interpretations about the anthropogenic causes of recent global warming should be cautious. Our polynomial cointegration tests challenge their interpretation of the data.