Streetwise Professor

January 6, 2013

Woulda, Coulda, Shoulda

Filed under: Climate Change,Politics — The Professor @ 4:02 pm

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.

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  1. You probably meant to write ‘I(1),’ not ‘I(0)’; I(0) processes are stationary.

    Comment by Phil Rothman — January 7, 2013 @ 2:03 am

  2. I spent 3 months of an internship at a hedge fund a few years ago coming up with pricing method for weather derivatives. I noticed plenty of papers talking about fractional integration & I(1) for weather modeling (atleast from a pricing perspective) 🙂

    Comment by Surya — January 7, 2013 @ 8:21 am

  3. Yes, climate change data has a lot in common with economic data (observational, possibly nonstationary, etc.), so time series analysis should be very useful. Indeed, a paper a few years ago from econometrician Tim Vogelsang finds that, using appropriate tests (when the errors -innovations-may or may not be stationary) there is a positive trend but it is very small. I haven’t seen anything about cointegration but I agree that the CO2-warming link is a good candidate for spurious regression.

    From the abstract: ”The point estimates of the rate of increase in the trend suggest that temperatures have risen only about 0.5 degrees Celsius (1.0 degree Fahrenheit) per 100 years.”

    Comment by Jack — January 7, 2013 @ 9:46 am

  4. You need to look further up the statistical evidence chain. Obviously, there are no little thermometer hiding in the rings of trees or in the strata of ice core samples. The modelers try to derive what the temperature was historically with the use of assumptions and surrogates. I have looked scatter diagrams of some of these surrogates Vs Temp. The resulting charts looks more like a cloud than a lines. I guess modelers could forecast anything they want provided they control the assumptions. Remember when financial modeler assumed that house prices only rise?

    Comment by Steve — January 7, 2013 @ 2:24 pm

  5. You’re right, @Phil. Got ahead of myself. Changed now.

    @Steve. I wrote a post several years ago in which I made comparisons between climate models and models used in economics and finance, e.g., old school multi-equation macro models and models for CDOs. Climate modelers are like the Wizard of Oz.

    Re clouds vs. lines. You just have to be “creative” with your use of principal components, to extract a powerful signal from that cloud of noise 😛

    The ProfessorComment by The Professor — January 7, 2013 @ 4:19 pm

  6. @Steve. Here’s the post I was thinking of. Crikey! 6 freaking years ago. Time do fly.

    The ProfessorComment by The Professor — January 7, 2013 @ 4:29 pm

  7. Even an extremely optimistic Doha climate outcome would have cost $500 billion annually, with benefits of less than five cents on the dollar. A modest Doha free-trade agreement, by contrast, could help the world’s poor thousands of times more, much sooner, and at a much lower cost.

    Yes, we need to tackle climate change – and tackle it smartly. But the Doha climate talks were always a dead end. If we really want to help the world’s poor, we should get serious about the other Doha talks.

    Comment by Peter — January 8, 2013 @ 9:36 am

  8. I never cease to be amazed that, while nobody in the real world can predict population, energy price or the nature of technological innovation 100 years into the future (and has never been able to throughout human history), state-funded climate scientists can now do just this – with such accuracy that they can predict the extent of global warming to within tenths of a degree.

    Furthermore, although the science is settled and there’s no room for doubt, they still need to have taxpayers’ money firehosed at them to make it even, well, even more settled, I suppose.

    Why aren’t they traders instead of second-rate scientists? With this degree of insight into the future, they could all be millionaires, surely?

    Comment by Green as Grass — January 8, 2013 @ 12:31 pm

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