After the last post I expected a firestorm of commentary about Donald Trump. Personally, I’m not very fond of Donald Trump.
Putting aside some of GreenHeretic’s nonsense which commenters have already addressed, he rejects linear regression to establish that the temperature trend (actually he refers to its relationship to CO2) is statistically significant. Why? Because the residuals fail the Durbin-Watson test.
That means those residuals exhibit autocorrelation. He even confirms this himself by computing the autocorrelation function. The horrid mistake is his conclusion from this: that “Estimates or inferences that depend on error variance are suspect, at best. That includes any tests of statistical significance. The errors are not independently and identically distributed (iid).”
He seems to be yet another who thinks (the first I’m aware of was our old friend Tim Curtin) that this invalidates linear regression. It doesn’t. It does require that we compensate for autocorrelation, both when evaluating statistical significance and when estimating probable error ranges. When you do so, you find that statistical significance is still quite real. Evidently, GreenHeretic doesn’t know how to do this.
His other mistake is to substitute an ARIMA(1,1,0) model. I’ll bet he learned that in econometrics class. The “1” in the middle makes it a first-difference model, which is how they tend to deal with trends. It also means that the ARIMA model has what’s referred to as a “unit root.”
Curiously, as intent as he was on applying significance tests to anything that shows a trend in temperature, he doesn’t report any tests of his first-difference model. A natural thing to do is to ask whether or not that unit root is real.
That’s not easy to establish; tests for unit root generally have very little power, so even if there is no unit root it’s hard to reject the idea. But in this case, the unit root is so thoroughly absent that the idea is rejected easily. The Phillips-Perron test, e.g., rejects it resoundingly. GreenHeretic’s model simply does not apply.
To sum up: First, he rejects linear regression, not because it isn’t valid but because he doesn’t know how to deal with autocorrelation. Second, he puts his faith in a first-difference model which is easily shown to be invalid.
My opinion is that “GreenHeretic” is a fine example of the phenomenon referred to as Dunning-Kruger.
I’m also of the opinion that there’s less and less value in refuting arguments from the ignorant which are rooted in mathturbation. Rather than refute you, let’s forget you, better still.