I had thought in my last post that it was quite evident that the model in Rahmstorf 2007 was not well specified. In fact I was more interested in the issues dealing with the response to comments than I was in making the point clearly I suppose.
In that post I showed that the first half of the data did not do a good job of predicting the second half of the data. In fact the coefficient for the second period has half the value of the first period which would produce wildly different results for future predictions. But this by itself doesn't show the obvious which is that the linear model just doesn't work even without looking at out of sample prediction.
Here is a web page that presents the methodology for whether a linear regression is well specified.
Remember that I am doing this against the final calculations with corrections from the corrigedums by Rahmstorf.
First I plotted predicted values against the actual values, and in fact they are not symmetrically distributed around either the diagonal or horizontal line. You can try it yourself from the code I already posted. But since there is no fixed rule for what symmetric means, my experience is that this will not be sufficient to make my point.
So then I computed the Durbin Watson statistic for autocorrelation in the results.
The result is .4 which according the Wikipedia page puts it in the range where it "might be cause for alarm."
The point is that the residuals are not well scattered, and they are highly autocorrelated. This should be enough for anyone to see that even a first year statistics student would know that the model isn't well specified.
In response to a comment here is the plot of the actual versus predicted values.
Here is a plot of the residuals. It doesn't take a DW statistic to see how highly autocorrelated they are.