Comments on: Variance Stabilization in Esper Chronologies

By: John A

John A — Thu, 23 Feb 2006 09:39:31 +0000

My “Eyeball Technique” tells me that there is no climatic significance to any of the Esper series. Should I publish?

By: Ross McKitrick

Ross McKitrick — Thu, 23 Feb 2006 01:32:10 +0000

Steve, by rescaling them to have a mean 0 and sd=1 over the series length, that might understate some of the differences. Shouldn’t you rescale them to the mean and sd over the post-1901 subsegment? (Just kidding!)
What I’d rather see would be the Goldfeld-Quandt stats for each series. And, if homoscedasticity is suddenly so important, let’s hear an a priori declaration (without peeking at the results) from the tree ring experts of what the cut-off is that disqualifies a series. But beyond that, as you pointed out earlier, someone needs to provide a model to explain why we would not expect tree rings chronologies to exhibit ARCH behaviour, especially since they are otherwise known to be strongly autocorrelated. If there’s some reason to believe that a valid proxy would not reject a null of no-ARCH, then a gauss-newton regression is easy to do and generates F stats that settles the matter. Again, if paleoclimatologists really believe this is a legitimate selection criteria, let them pick the p-value for the F stat before peeking at the answers.
Even if one accepts an eyeball argument for the Yamal switcheroo, then the Yamal series looks like it should be truncated at around 1900.

By: John S

John S — Thu, 23 Feb 2006 00:37:21 +0000

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?