Back in the mid-to-late-1990s, when I first started reading about global warming (which has since be relabeled to the more, umm, flexible “climate change”), one thing that struck me is that estimations of temperature trends were statistically daft. The temperature data appeared integrated, that is, non-stationary. (The data are I(0) I(1) technically.) This means that temperatures are characterized by “stochastic trends.” So estimating some sort of time trend, and projecting it into the future, is statistically nonsensical. The trends estimated in that way jump around randomly.
It surprised me that it didn’t seem that this had been recognized in mainstream climate science. I searched around a little, and found a Russian scientist (a hydrologist, I believe, but I can’t put my hands on his name or his book) who had written about this. (In a way, not surprising, because hydrological time series present interesting integration issues, including fractional integration.) We corresponded a few times, but the language barrier was a problem. And it seemed like he was a voice in the wilderness anyways. He wasn’t a climate scientist, and his book was obscure and badly translated.
Thinking about an integrated time series like temperature, and the theory that CO2 drives temperature, immediately brought to mind the question of whether temperature and CO2 are co-integrated. Cointegration would suggest some causal connection between these variables: a lack of cointegration would suggest no causal connection. Absent cointegration, the correlation between temperature and CO2 would be a case of “spurious regression.” Spurious regression occurs when two unrelated, but highly autocorrelated time series are regressed on one another. One way of thinking about spurious correlation is: are you going to believe your lyin’ eyes? The answer is no: just because two (integrated) time series seem to move together does NOT mean that there is any causal connection between them. Basically it means that the association between CO2 and temperature, which seems so compelling to the naked eye, is statistical garbage.
But I never pursued the idea, because, well, I had lots of other fish to fry and climate science was/is not my comparative advantage. Fortunately, years later-far too long, IMO-somebody has taken up the issue. Using more sophisticated techniques than I would have considered using, the authors of this paper demonstrate that temperature and anthropogenic variables (e.g., CO2) are not polynomially cointegrated. At most, they find that shocks to CO2 have a temporary impact on temperature.
This is a major problem for global warming absolutists, who see a mechanical connection between CO2 output and temperature.
And I am amazed that it’s taken so long for someone to have explored this rather obvious research path. But given the results . . . maybe not.
Note that most of the references in the paper are to the econometric literature. Time series econometricians have thought deeply about integrated time series for a long time. It’s about time for climate scientists to do the same. Actually, it’s well past time. About 15 years, at least.