In fact the hockey -
stick shaped PC was still there, but it was no longer the strongest PC (PC1), it was now only 4th - strongest (PC4).
Whether you use the MBH98 non-standard centering, or standard centering, the hockey -
stick shaped PC must still be included in the analysis.
The truth is that whichever version of PCA you use, the hockey -
stick shaped PC is one of the statistically significant patterns.
Not exact matches
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It even seems to me that
PC # 1 of short - centered red noise is likely to be hockey -
stick shaped (especially if one calls step changes a hockey
stick).
Yet even when I «jack up» the autocorrelation to ridiculously high values, the hockey -
stick -
shaped PC # 1 still doesn't come close to matching the strength of
PC # 1 from the MBH98 analysis of the NoAmer ITRDB proxies.
but by my calculations yes, you can get a hockey -
stick shape in the first
PC by applying short - centered PCA to red noise.
When MM applied PCA to the North American tree - ring series but centered the data in the usual way, then retained 2
PC series just as MBH98 had, lo and behold — the hockey -
stick -
shaped PC wasn't among them!
«A further aspect of this critique is that the single - bladed hockey
stick shape in proxy
PC summaries for North America is carried disproportionately by a relative small subset (15) of proxy records derived from bristlecone / foxtail pines in the western United States, which the authors [MM] mention as being subject to question in the literature as local / regional temperature proxies after approximately 1850.
He did this very experiment himself and discovered that the
PCs lose their hockey
stick shape when the Graybill - Idso series are removed.
Regarding the «Hockey
Stick Index» metric touted by M&M, that metric tells you only about the «shape» of the «hockey stick» PC; it tells you nothing about the hockey - stick «size&ra
Stick Index» metric touted by M&M, that metric tells you only about the «
shape» of the «hockey
stick» PC; it tells you nothing about the hockey - stick «size&ra
stick»
PC; it tells you nothing about the hockey -
stick «size&ra
stick «size».
What is missing in all this is whether the higher order
PC's that would have been derived from the red noise proxies, and included in the full PCA, would have eliminated the hockey
stick shape in the full representation of the data, using the correct number of
PC's.
In the MBH «common centered» method, the first
PC contains a noticeable «hockey
stick» - like
shape, whereas in the «full centered» method this
shape is spread across the first two
PCs.