Math101 – Filtering Theory

On August 27th 08, before August HadCRUT nh+sh temperature was available, I posted this prediction ( http://signals.auditblogs.com/files/2008/08/gmt_pred.txt ) at CA:

After four months, it is good to check how well the simple half-integrated-white-noise model is doing. Predictions for these 4 months were

Year        Month     -2 sigma     Predict.     +2 sigma
2008              8       0.15206     0.34864      0.54521
2008              9       0.1141       0.33388      0.55365
2008             10      0.094005    0.32581      0.55762
2008             11      0.080432    0.32024      0.56005

and observations today 15th Dec 08 on HadCRU website are the following:

2008/08 0.396
2008/09 0.374
2008/10 0.438
2008/11 0.387

Here’s how these fit to the original figure:

The model is doing quite good work. I’ll tell you when we reach the upper bound of the prediction interval. And after temperatures go permanently above that bound, AGW kicks this model to the trash can.