Wahl and Ammann 2006 reported that they could “get” something that was sort of HS-ish without principal component analysis. It wasn’t through a simple mean or CVM; it was through Mannian inverse regression. Juckes et al shows many reconstructions using “inverse regression”, mentioning in his conclusions that inverse regression caused over-concentration on a few proxies.
we have found that inverse regression tends to give large weighting to a small number of proxies and that the relatively simple approach of compositing all the series and using variance matching to calibrate the result gives more robust estimates.
This is not the only potential problem with inverse regression in this type of network. Here’s a diagram which I showed in my European trip to Juckes co-author Nanne Weber at KNMI. In the top left corner (magenta), I’ve shown a Mannian reconstruction using the 68 non-stripbark series in the AD1400 network; the two black series show Mannian reconstructions using AR1=0.2 red noise; the red series is the CVM of the 68 non-stripbark series. Visually the reconstruction using non-stripbark proxies is very similar to the reconstruction from the same method using red noise. Both methods give quite decent correlations in the 1902-1980 calibration period. Note that the Mannian regression method flips over the reconstruction using the average of the series.
Consider what this means for Mannian calculations in which confidence intervals are estimated using calibration period residuals. Yes, the Mannian calculation yields a standard error, but the standard error is not measurably lower in this case than the standard error from red noise. Also there is obviously not a HS without the stripbark samples.
Top left — WA variation on 68 non-strip-bark series; black — WA variation AR1=0.2 red noise simulations; red- average of non-strip-bark network
In another post, I’ll show what happens when you add in HS-shaped series. For now, I just wanted to illustrate in another format the meaninglessness of the Wahl and Ammann fit.
While the fit is meaningless, I think that there is a decent possibliity that the Wahl and Ammann no-PC regression could become a statistical classic as one of the most remarkable examples of overfitting that I’ve encountered.