In today’s post, Jean S and I are going to show that the paico reconstruction, as implemented in the present algorithm, is very closely approximated by a weighted average of the proxies, in which the weights are proportional to the number of measurements. Paico is a methodology introduced in Hanhijarvi et al 2013 (pdf here) and applied in PAGES2K (2013). It was discussed in several previous CA posts.
We are able to show this because we noticed that the contributions of each proxy to the final reconstruction can be closely estimated by half the difference between the reconstruction and reconstructions in which each series is flipped over, one by one. This sounds trivial, but it isn’t: the decomposition has some surprising properties. The method would not work for algorithms which ignore knowledge of the orientation of the proxy i.e. ones where it supposedly doesn’t “matter” whether the proxy is used upside down or not. In particular, the standard deviations of the contribution from each proxy vary by an order of magnitude, but in a way that has an interesting explanation. We presume that this decomposition technique is very familiar in other fields. The following post is the result of this joint work. Continue reading