## Variance Stabilization in Esper Chronologies

Yesterday, Science sent me 13 Esper site chronologies, all standardized using RCS methods, one of which is the updated Polar Urals site. It’s hard to think of a better testing ground for Rob’s argument that the variance of the Polar Urals series disqualified it and mandated the substitution of the hugely hockey-stick shaped Yamal series. See http://www.climateaudit.org/?p=541

In the spirit of spaghetti graphs, I have calculated 101-year moving variances for all 13 Esper sites, along the lines of Rob’s graph. I then scaled them all to have a mean of 0 and standard deviation of 1 . Here’s what I got, with the Polar Urals series shown in heavy black. Using the dendroclimatological statistical technique of "eyeballing", I do not observe any reason why the Polar Urals series is particularly problematic.

Figure 1. Spaghetti graph of 101-year moving standard deviations (scaled).

The red series caught my eye as it seemed to have a lot of similarity to the Polar Urals series in range. So I’ve plotted it and the Polar Urals series below. Guess what it was – the usual companion to Polar Urals: Tornetrask. So the variance at Polar Urals does not seem at all unusual relative to Tornetrask.

Figure 1. Non-spaghetti graph of 101-year moving standard deviations (scaled) for Polar Urals and Tornetrask.

1. John S

Rolling standard deviations on a series with significant trends? I just don’t get it. If you have trends or cycles that have a period of greater than the window you use, the mean/trend effect is just going to swamp calculations of standard deviations.

Consider:
X(t)=t+epsilon (i.e. a linear trend plus noise)

epsilon=N(0,1)
and Y(t)=epsilon

Compare the standard deviation of these two series over any window and you will find that X(t) is much more variable than Y(t), but it doesn’t really tell you much. Indeed, it seems that selecting on stable variance is a recipie for squashing any actual signal in the series. I must be missing something. What am I missing here?

2. Ross McKitrick