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Steve Bloom points to Comment on “Polynomial cointegration tests of anthropogenic impact on global warming by Beenstock et al (2012)".  Some fallacies in econometric modelling of climate change" D. F. Hendry and F. Pretis.

Now Eli has to admit a bit of shame about this one.  The bunny got tangled up in the mathturbation.  James, in his usual laconic way was the closest

Were I Judith Curry, I would probably be saying "wow" at this stage. Alternatively, it could just be some dross that has accidentally found its way into print after having been rejected at least twice at different journals.

The review comments are interesting, to say the least. Reviewer #2, in particular, seems awfully keen on a number of silly sceptic claims that have been presented in recent years.

I suppose it just goes to show that you can fool at least one person sometimes, and if that person happens to be a journal editor, you're in luck.

Those of you who remember Eli and Socrates going around on statistics know the answer

 [Eli] In other words, if you have a good idea of the answer they can help you, but if not you need physics or biology or chemistry or meteorology.

Hendry and Pretis, smart bunnies, didn't look at the econometric analysis, they looked at the data set.  Why you ask, well, anyone who studies blog scientists knows why

In their analysis of temperature and greenhouse gases, Beenstock et al. (2012) present statistical tests that purport to show that those two variables have different integrability properties, and hence cannot be related. The physics of greenhouse gases are well understood, and date from insights in the late 19th century by Arrhenius (1896). He showed that atmospheric temperature change was proportional to the logarithmic change in CO2). Heat enters the Earth’s atmosphere as radiation from the sun, and is re-radiated from the warmed surface to the atmosphere, where greenhouse gases absorb some of that heat. This heat is re-radiated, so some radiation is directed back towards the Earth’s surface. Thus, greater concentrations of greenhouse gases increase the amount of absorption and hence re-radiation. To “establish” otherwise merely prompts the question “where are the errors in the Beenstock et al. analysis?”.

In other words, the Beenstock et al don't know anything about the system they are studying.  In particular, point out that the data series used for greenhouse gas concentrations, is not a single series but a compilation, and that the nature of the data changes over about 1960 from ice cores to atmospheric grab samples
Interacting with unmodelled shifts, measurement errors can can lead to false interpretations of the stationarity properties of data. In the presence of these different measurements and structural changes, a unit-root test on the entire sample could easily not reject the null hypothesis of I(2) even when the data are clearly I(1). Indeed, once we control for these changes, our results (see Tables 1 and 2 below) contradict the findings in Beenstock et al. (2012)


 Once that is done, and one actually looks at the data, it becomes clear that there are two separate  periods during which the properties of the correlation between temperature and forcing changes, roughly divided at 1960, and that Beenstock's analysis depends on an incorrect pooling of data.

Econometrics is a hammer which econometricians apply to all objects, but  it's ALWAYS the science that rules.