Although this is a very thoroughly analysis, my understanding, albeit limited, of ARIMA modeling (or just ARMA in this case) with covariates makes me believe that the procedures of model identification is flawed.

The authors appear to model the covariates then identify the ARIMA parameters. I was under the impression that you identify a stationary time-series process for both the the DV and IV variables then find the cross-dependence of the variables. In this case, the ARIMA parameters are modeled with the covariates.

I don't find this especially problematic until they remove the CO2 as a predictor; this assumes that these are the same ARIMA parameters as the previous mode, when that may not be the case. I think this is why fitting the time-series models first, then adding the predictors is a better procedure. Regardless, not attempting to verify, and possibly reidentify, the ARIMA process seems suspect to me. Therefore, the comparison with the model without CO2, and their subsequent interpretations, may be based on a misidentified model. And although I'm a big fan of bootstrapping, jackknifing, and whatever other resampling or simulations techniques one can use to improve their study, they still require careful modeling by the researchers. Using resampling based on a misidentified model will lead to a robust estimate of the parameters, but misidentified parameters.

Anyways, this is just my evaluation of their modeling techniques. They may be generally correct, but I think their methodology could be improved before feeling as confident as the authors are, not to mention I'm sure some will misinterpret what the authors meant by 99.999% (i.e., p-values and effect sizes may be related but are surely not synonymous).

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Posted by Taxing Authority

Houston

Member since Feb 2010

57455 posts

Posted on 9/9/14 at 2:38 am to buckeye_vol

quote:
buckeye_vol

Thanks for the contribution to the tribal echo chamber! I'm not sure they were searching for cross dependency as much as they were trying to eliminate it as a possibility. Keep that in mind.

The problem I have with this is the choice of input parameters. They chose a whopping four variables to model the climate with. Only one displays an exponential response (CO2). Then go through the ruminations of saying it correlates best to the presumed temperature anomaly.

Conceptually, that's kind of a "duh". In reality, they could have chosen population (below) and shown that it was the best fit of the four.

Corn crop yields would probably have worked too.

Perhaps the housing price index?

Maybe too flat at the beginning...

I realize I'm dumbing this down a lot. But it is a 4-variable model. Conceptually, I don't see how it could have come to a different conclusion given the inputs. GIGO is a risk.

I wish there were more discussion on residuals. I *do* see a spike c.1940 (good!), but the duration is much shorter than the 40s Bump. And I'd expect to see a rise at the end accounting for "the pause". Those are pretty solid landmarks for when the CO2/temperature correlations have have gone wonky. I'd expect the modeling to go wonky too, or, have a suitable input. Could be as simple as a time slice issue, or washed out with regression(