Look interesting. Let’s continue:

Inspired by Dave’s comment , I made a hockey-stick plant, code here . It produces this kind of pictures:

Millennium project cost is 15 million euros (2006-2009). They say

Our multi-disciplinary team will use innovative and developing technologies to extract quantitative palaeoclimate information from documentary and natural archives, including trees, lakes, mires and ice cores

If the questions raised here are not handled properly, I want my money back. That will be 0,03 euros.

The calibration period runs from about 1860-1980, and the 100 year trailing cross-correlation data for that period is shown by the blue lines … I don’t think we need a lot of sophisticated math to determine whether the MITRIE reconstruction is statistically significant …

The pre-calibration period average cross-correlation is 0.04, while that of the calibration period is more than three times that, 0.14.

w.

#78 complained that the very notion of selecting sites for their sensitivity to temperature was
flawed. I pointed out that this technique was valid.

The problem with the analogy that you used is that you knew a-priori that the store did not sell shoes, relying on pants for income instead. We don’t have that a-priori knowledge w.r.t. trees and their ring widths, hence statistical analysis. Therefore, selecting one tree because it responds well to a specific climate variable, while excluding another, is really an end-run around what should really be done: exclude the hypothesis (or accept the null, which is no correlation).

I never meant to imply that trees were, or were not good proxies for temperature.

Yes, I got that part. Should we manage to contrive a controlled experiment, they probably could be.

Mark

PS – It strikes me writing this that we should be able to distinguish red noise from signal by comparing the average inter-series correlation during the calibration period to the same statistic during the rest of the earlier record … but I haven’t a clue what would be a valid test statistic for the comparison, particularly since the number of data points decreases with age

That is a good question. Monte Carlo simulations are one option.

But let’s try to write down what should happen: Assume N independent red-noise processes, and those processes have identical autocorrelation structure. Then it is easy to show that the average process (*) has similar autocorrelation structure, but the process variance is reduced by a factor of 1/N. If the autocorrelation structure varies, then computations are not that straightforward. But the variance of the average process is 1/N of the mean variance of the original processeses. And if those original processes are standardized, the 1/N reduction works, whatever the autocorrelation structure is. Thus, if for given data the variance gets down by 1/N in the verification period, but not that much in the calibration period, we should be worried about overfitting.

And this here’s the funny part, it means that we should be worried about overfitting if the result is hockey-stick shaped!!

See also Dave’s comment
http://www.climateaudit.org/?p=1283#comment-98150

(*) A new stochastic process that we obtain by taking average over N processes.