In my previous comment on Ritson’s AR1 calculation, I think that I correctly diagnosed that the calculation was goofy, but I didn’t diagnose what was going on correctly (thanks to Demetris Kousoyannis who emailed me). I’ve re-visited it and I’m pretty sure that I’ve now diagnosed the problem with what Ritson was doing. My starting premise was 100% correct – if you simply do an AR1 fit to the US tree ring series, you get the high AR1 coefficients that I reported before and which differ radically from the Ritson coefficient. So you have to ask yourself: if there’s a perfectly good algorithm for calculating AR1 fits, why does Ritson propose a new algorithm for calculating an AR1 coefficient? Why wouldn’t he just use a standard algorithm? Needless to say, I am naturally pretty suspicious of Hockey Team non-standard algorithms?
Anyway, I checked Ritson’s method against synthetic AR1 series of varying AR1 coefficients up to and including random walk and, while the answers were different than those of a standard algorithm, they were all in the right general range.
Then I experimented with ARMA(ar=.9,ma=-0.6) noise, a type of noise pretty familiar from climate time series (leaving aside the larger question of long-term persistence and multiple scaling). ARMA (1,1) series are something that should be on the radar screen even of the Hockey Team.
Here the performance of the various methods varied fantastically. This is based on very quick simulations. If you correctly specified the model as ARMA(1,1), estimates of the AR1 coefficient using standard arima function in R were 0.8-.93, all pretty reasonable. If you estimated the AR1 coefficient using a mis-specified ARMA(1,0) model, you got AR1 coefficients in the 0.34-0.53 range, which, interestingly enough, is also in the range of observed AR1 fits to North American tree ring data.
Now for the Ritson coefficient: it was in the 0.0 to 0.2 range, again almost exactly the Ritson coefficients for the North American tree ring network. So the Ritson method fails catastrophically in the face of ARMA(1,1) noise. A conventional AR1 calculation is a little more stable against misspecification of ARMA(1,1); the Ritson method goes haywire.
Of course at bizarroclimate, they won’t care about such details.
It’s never easy with the Hockey Team.