I recommend that CA readers visit UC’s blog for some interesting discussion. (BTW UC visited Toronto recently and we had a nice dinner.) UC posted the following interesting figure on Unthreaded as follows:
BTW, got interesting result when I replaced Temperature PCs with solar in MBH98 algorithm. Similar RE values as in the original, and R2 goes down in the verification. I’d try this with 1980-present data, but the proxies are not yet updated.
This intrigued Pete H who inquired:
I wonder what other data series could be plugged in to good effect? We could create a nice quilt of hockey stick graphs. A great way to demonstrate the extreme confirmative value of todays influential real climate science.
I can give a pretty complete answer to this, drawing primarily on an early answer to this question, since many, if not most present readers, were not around a couple of years ago. This post discussed the regression phase of MBH98-99, which has its own place in the MBH little shop of horrors.
The figure below shows 6 “reconstructions” using different combinations of a Tech Stock PC1 or the MBH98 North American PC1 in combination with the other proxies in the MBH98 AD1400 network or white noise. For the purposes of “getting” a high RE statistic – the sole arbiter of Mannian success, it didn’t “matter” what combination you used. Other than the North American PC1 – essentially the bristlecones, it didn’t matter whether you used the other proxies or white noise. And it didn’t matter whether you used Tech Stocks or bristlecones.
Here’s the figure from the earlier post.
Figure 3. Left – Tech stocks; right – MBH. Top left – Tech PC1 (red), MBH recon (smoothed- blue). Top- Tech PC1 and Gaspé-NOAMER PC1 blend; Middle – plus network of actual proxies; Bottom – plus network of white noise.
I explained the experiments as follows:
To test the difference between MBH98 proxies and white noise, I tried the following experiments, illustrated in Figure 3 below (see explanation below the figure). I discuss RE results – the “preferred” metric for climatological reconstructions for each panel. As a benchmark, the RE statistic for the MBH98 AD1400 reconstruction (second right) is 0.46, said to be exceptionally significant.
Some time ago, I posted up the “Tech PC1″, which I obtained by replacing bristlecones with weekly tech stock prices, as an amusing illustration that Preisendorfer significance in a PC analysis did not prove that the PC was a temperature proxy. I re-cycled the Tech PC1 to compare its performance in climate reconstruction against that of the NOAMER PC1 (actually a blend of the NOAMER PC1 and Gaspé – the two “active ingredients” in the 15th century hockeystick.
In the top panels, I fitted both series against NH temperature in a 1902-1980 calibration period. The top right panel shows the Tech PC1 (red), together with MBH (smoothed- blue) and the CRU temperature (smoothed- black). The “Tech PC1″à actually a higher RE statistic (0.49) than the MBH98 reconstruction (0.46), but it does have a lower variance (in Huybers’ terms). The Tech PC1 has an RE of 0.49, slightly out-performing both the NOAMER PC1-Gaspé blend (RE: 0.46) and the MBH98 step itself (RE: 0.47). In the most simple-minded spurious significance terms, this should by itself evidence the possibility of spurious RE statistics. Both the Tech PC1 and the Gaspé-NOAMER blend have less variance than the target (and the MBH98 reconstruction itself.)
The second panesl show the effect of making up a proxy network with the other MBH98 proxies in the AD1400 network. In both cases, variance is added to the top panel series, in exactly the same way as in the examples with simulated PC1s. The RE for the Tech PC1 is lowered slightly (from 0.49 to 0.46) and remains virtually identical with the RE of the MBH98 reconstruction.
Now for some fun. The third panel shows the effect of using white noise in the network instead of actual MBH proxies. In each case, I did small simulations (100 iterations) to obtain RE distributions. For the “Tech PC1 reconstruction”, the median RE was 0.47 (99% – 0.59), while for the MBH98 case, using the NOAMER-Gaspé blend plus white noise proxies, the median RE was 0.48 (99% – 0.59). Thus, in a majority of runs, the RE statistic improves with the use of white noise instead of actual MBH98 proxies. The addition of variance using white noise is almost exactly identical to the addition of variance using actual MBH98 proxies.
The concluding comment was interesting and worth following up:
These results, which I find remarkable, tell me a lot about what is going on in the underlying structure of MBH98, which was, if you recall, a “novel” statistical methodology. Maybe the “novel” features should have been examined. (Of course, then they’d have had to say what they did.)
When I see the above figures, I am reminded of the following figure from Phillips  , where Phillips observed that you can represent even smooth sine-generated curves by Wiener processes. The representation is not very efficient Phillips’ diagram required 125 Wiener terms to get the representation shown below.
Figure 4. Original Caption: The series on extended periodically.
Phillips’ Figure 2 is calculated using 1000 observations and 125 regressors. In the MBH98 regression-inversion step, the period being modeled is only 79 years, using 22 (!) different time series (a ratio of 4), increasing to use even more “proxies” in later periods. My suspicions right now is that the role of the “white noise proxies” in MBH98 works out as being equivalent to a “representation” of the NH temperature curve more or less like Figure 2 from Phillips. The role of the “active ingredients” is distinct and is more like a “classical” spurious regression. I find the combination to be pretty interesting.
Essentially what Mann did was to create a form of multivariate spurious regression. Traditional spurious regression – the type that you read about in Granger and Newbold 1974, Phillips 1986 – the type that econometricians are used to is univariate. Mannian spurious regression is a generalization of univariate spurious regression. You take one spurious regression (between Tech Stocks and NH temperature) between two unrelated trending series; and then insert this together with a large number of essentially white noise series (low-order red noise also works) in the Mannian multivariate method and bingo what have you got?
1) a high RE statistic
2) a negligible verification r2 statistic;
3) a high calibration r2 (and thus low standard errors in the calibration period)
4) seemingly narrow confidence intervals based on the low residuals in the calibration period.
It is, of course, a complete farce. The “no-PC” reconstruction bruited by Ammann and Wahl completely misunderstood the problems with the technique and carried it to an extreme that is almost a satire. Statistics by Monty Python, so to speak.