I find it difficult to believe that so many scientists have seemingly accepted the realclimate argument that Preisendorfer’s Rule N applied to a principal components calculation is somehow a substitute for proper statistical analysis. To show the goofiness of this argument, I asked a friend to compile a list of weekly closing prices for 20 tech stocks in the bull market. Of these, there were 15 stocks with at least 581 values. I then substituted 15 tech stock prices for 15 bristlecone pines in the NOAMER tree ring index. The results are pretty funny.
Figure 1 shows the first 4 PCs using the MBH98 principal components method. The PC1 has an obvious hockey stick shape. It is comprised almost entirely of tech stock prices. It is even more strongly correlated to the "climate field" than the PC1 with bristlecone pines in it. I’ve not carried through a full emulation yet, but I’m pretty sure that it will yield a MBH98-type hockeystick in the full emulation as well. The PC1 is "significant" under the Preisendorfer Rule N, which Mann et al. reported in December 2004 to have been used in tree ring networks, but obviously weekly tech stock prices are not a "proxy" for 1400-1980 temperature.
Figure 2 shows the first 4 PCs under a centered PC calculation. In this calculation, the PC1 looks pretty much like the PC1 in the NOAMER AD1400 network (and like the PC4) in the "NOAMER plus tech" network. Here the tech stocks affect the PC3 and impart a hockey stick shape to the PC3. There’s an uncanny parallel to the bristlecones being demoted in a centered calculation. I haven’t done the Preisendorfer calculation yet, but the PC3 (dominated by tech stocks) will almost certainly be "significant" under Preisendorfer.
If the example seems ridiculous, it is less ridiculous than the Preisendorfer argument, which is now the sole thread which Mann, Gavin Schmidt, Caspar Amman etc. are relying on.
Climate Audit 
8 Comments
Steve,
You once commented that hockeysticks in financial prospectuses for dubious investment vehicles were a usual sign that all was not well. Do you have any examples of those?
John, not handy. They were more frequent in the 1990s. Hockey stick revenue projections would tend not to be in the prospectus itself but in more ephemeral promotional literature. You’d also see them in private offerings, done by offering memorandum rather than prospectus (which is an important distinction in securities offerings.) Steve
These are very useful graphs, thanks, Steve. Did not you want to include PC5, too? Have not they used PC5? I suppose that it is no accident that on figure 1, PC1 and PC2 are strongly anti-correlated, and the directions could also happen to be the other way around if you took data from a bear market, could not it?
If a result is not robust against elimination one type of data – like all bristlecone pines – or against elimination of one PC, then it’s not trustworthy. The temperature reconstructions from one particle type of trees may be entirely wrong – it is more or less guaranteed on statistical grounds that for *a* type of proxies, the method gives systematically misleading results. Putting a lot of bristlecone pines to the ensemble may increase the psychological illusion that things are robust, but it does not change the reality of the robustness, does it? It almost reminds me our debates about the anthropic principle – where some people argue that if they can create many (different, in detail) versions of a model XY of string theory, then it means that we should take the features of XY more seriously (regardless of the fact that the goal of science is not to generate many versions of the truth; and that many versions could also be constructed out of other answers).
The PC1 and PC2 will be orthogonal by terms of the calculation, but I see what you mean- they certainly appear anti-correlated. PC methods are not really designed for time series. In the realclimate debate, it’s the PC4 that matters in a correct calculation – it’s the carrier for bristlecones. That’s why I only illustrated 4 PCs. But the point was more to illustrate that Preisendorfer “significance” is a different thing than proving something is a temperature proxy.
I wish I could say that the image from string theory helped me, but I don’t know anything about string theory.
You’ll notive how Mann et al have completely evaded the issue of non-robustness to bristlecone pines – even though they claimed that their recosntruction was robust to the presence/absence of all dendro indicators. When pressed on this, Mann changes the topic and argues that , by robsutness, he means that other Hockey Team results are similar.
Regards, Steve
What does the hockey stick figure plot? PC1 or a summation of PCs? And what is the relevance of a PC “signal” to the actual record of temperature? Means seem more relevant to what we care about, no? And when Mann talks about the PC4, does he mean the summation including PC4 would have a hockey stick shape or does he want each PC plotted. And when he does will he label that this is not temperature versus time, but some weird stat thing?
He wants the PC4 in by itself, since it has a hockey stick shape (which he doesn’t want diluted with other shapes). In his regression phase, theres another data mining operation and the hockey stick shape dominates the reconstruction whether it comes from the PC1 or the PC4. But it’s still bristlecones in the PC4.
WTF? That’s not a plot of temperature versus year, then!
Actually it seems a good reason to criticize even the plot of PC1 in the initial article.