He regresses temperature time series against a variety of predictor variables, concluding that there is no real influence of “non-condensing greenhouse gases” (i.e., GHG except water vapor) like CO2. He achieves this by rejecting regression of temperature in favor of regression of the first-differenced temperature data. You get that by taking the difference between each data value and its predecessor.
I’m puzzled by some claims Curtin makes about what’s required for a valid regression:
In general, the various rules or conditions that must be satisfied for a valid regression are the following:
(1) the predictor samples xt1,2…n and yt must be representative of the population that they are sampling;
(2) the unknown ut must have zero mean;
(3) the predictors must be linearly independent;
(4) the unknown ut must be uncorrelated;
(5) the unknown ut must be samples from a random variable population with constant variance, or homoscedastic.
It’s not so. Predictors don’t have to be linearly independent. Extreme lack of independence complicates regression and can lead to mistaken results, but it can be dealt with, and mild lack of independence isn’t really a problem. The error terms (what he calls “ut”) don’t have to be homoskedastic — that’s what weighted regression is for — or uncorrelated — that’s what generalized least squares (GLS) is for. You can even do ordinary least squares (OLS) with heteroskedastic or correlated errors, but you need to compensate for those factors, and it’s not as precise as GLS.
What really puzzles me is the way he rejects regression with the un-differenced variables. His first regression is temperature (GISStemp) against greenhouse-gas climate forcing:
I first regress the global mean temperature (GMT) anomalies against the global annual values of the main climate variable evaluated by the IPCC Hegerl et al.  and Forster et al.  based on Myhre et al. , namely, the total radiative forcing of all the noncondensing greenhouse gases [RF]
Annual (Tmean) = a + b[RF] + u(x) …. (3)
The results appear to confirm the findings of Hegerl et al.  with a fairly high R2 and an excellent t-statistic (>2.0) and P-value (<0.01) but do not pass the Durbin-Watson test (>2.0) for spurious correlation (i.e., serial autocorrelation), see Table 1. This result validates the null hypothesis of no statistically significant influence of radiative forcing by noncondensing GHGs on global mean temperatures.
The Durbin-Watson (DW) test is based on computing the statistic
It’s an estimate of , where is the autocorrelation at lag 1. If the noise is white then and the Durbin-Watson statistic is about d = 2.
The actual value of d is compared to critical values of the Durbin-Watson statistic. There are two critical values for each sample size and number of regressors, dL and dU. If d is less than dL, we reject the null hypothesis of no positive autocorrelation. If d is greater than dU we do not reject the null hypothesis. If d is between dL and dU the test result is inconclusive.
But Curtin says “do not pass the Durbin-Watson test (>2.0)” as though all values of d less than or equal to 2 confirm the existence of autocorrelation. That’s just plain wrong.
The DW statistic for his first regression is d = 1.749. For his sample size with one regressor, the critical values at 95% confidence are dL = 1.363 and dU = 1.496. Since d is greater than dU, we do not reject the null hypothesis of uncorrelated errors.
This test gives no evidence of autocorrelation for the residuals. But Tim Curtin concluded that it does. He further concluded that such a result means no statistically significant influence of greenhouse gas climate forcing (other than water vapor) on global temperature. Even if his DW test result were correct (which it isn’t), that just doesn’t follow.
Curtin’s next regression is of the first-differenced versions of his previous variables. This time he reports a DW statistic of 2.760 and states that it “passes the Durbin-Watson test statistic.” Apparently he concludes this because d exceeds 2. He further concludes that this regression is therefore valid, so the lack of significant response of (first-differenced) temperature to (first-differenced) climate forcing indicates no relationship.
Now for the really interesting part. The DW test can also be used to detect negative autocorrelation (in which successive values tend to be anticorrelated rather than correlated). To do so, you use the value 4-d for the test rather than d. For his result we have 4-d = 1.24. Now the critical values are dL = 1.352 and dU = 1.489 (they’re different because there’s one fewer data point in the differenced time series). Since 4-d is less than dL, we reject the hypothesis of no negative autocorrelation.
In other words, the regression which Curtin said fails the DW test actually passes, while the regression which he said passes, actually fails.
And — the presence of autocorrelation doesn’t invalidate regression anyway.
I have to wonder what kind of “peer-reviewed” scientific journal would publish this. Who were the referees for this paper?
It’s amusing to look at the Appendix to Curtin’s paper. He seems to be confused in his use of units. Apparently his readers might be too, since he feels the need to define the Joule as a unit of energy and Watt as a unit of power. Real scientists are supposed to know that already. So, who’s reading this “scientific” journal anyway?