Den stora tråden om global uppvärmning/växthuseffekten

I thought I'd play around with some randomly generated time-series and see if I could 'reconstruct' northern hemisphere temperatures.

I first generated 1000 random time-series in Excel - I did not try and approximate the persistence structure in tree-ring data. The autocorrelation therefore of the time-series was close to zero, although it did vary between each time-series. Playing around therefore with the AR persistent structure of these time-series would make a difference. However, as these series are generally random white noise processes, I thought this would be a conservative test of any potential bias.

I then screened the time-series against NH mean annual temperatures and retained those series that correlated at the 90% C.L.

48 series passed this screening process.

Using three different methods, I developed a NH temperature reconstruction from these data:

1. simple mean of all 48 series after they had been normalised to their common period
2. Stepwise multiple regression
3. Principle component regression using a stepwise selection process.

The results are attached.

Interestingly, the averaging method produced the best results, although for each method there is a linear trend in the model residuals - perhaps an end-effect problem of over-fitting.

The reconstructions clearly show a 'hockey-stick' trend. I guess this is precisely the phenomenon that Macintyre has been going on about.