I did an ARMA (1,1) on the CRU monthly (as opposed to the usual annual) global data set to see what it looked like. The ARMA (1,1) coefficients for the GL data for the second half of the data set were similar to those observed in the satellite data (AR1 +0.93; MA1 -0.46), but were different in the first half (AR1 +0.71; MA1 -0.27). The "look" of the persistence in the 19th century was quite a bit different than in the 20th century. I don’t see why the ARMA(1,1) structure should change with increased temperatures or increased CO2 and I wonder how much of this is due to measurement issues. It may be an interesting quality control cross-classification.
Here’s another interesting calculation – the AR1 and MA1 coefficients for all CRU gridcells by gridcell (this is from the July 2003 CRU dataset). There seems to be a strong ARMA (1,1) structure to the underlying temperature data(whatever the basis) – it seems plausible that ARMA (1,1) outliers would be an interesting form of quality control on the CRU data set: I wonder what causes the outliers, which are obviously more prevalent in higher latitudes. I can see weakening of the AMRA(1,1) structure away from the tropics, but negative AR1 coefficients are surprising.
Figure 1. ARMA (1,1) Model for CRU Gridcell Temperature Data By Latitude. Top: AR1 Coefficient; Bottom – MA1 Coefficient.