Tamino has been looking at the question of statistical significance in the temperature records. The good news is that he appears to agree with many on the sceptic side of the debate that AR1 is not a suitable model - it's always nice to find some cross-party consensus, particularly when this suggests that the IPCC is wrong. Tamino's preference is for an ARMA(1,1) model.
However, Doug Keenan emails to say that he has been trying to leave a comment suggesting another model:
The statistical model used above is a straight line with ARMA(1,1) noise. I do not know of a good justification for that model, and it is easy to find alternative models that have a far better statistical fit to the global-temperature data.One alternative model is fractional Gaussian noise (also known as "Hurst-Kolmogorov"). Good justification for fGn has been presented by Demetris Koutsoyiannis. In particular, fGn arises as a consequence of the second law of thermodynamics [Koutsoyiannis, Physica A, 2011]. The AIC value of fGn is also far lower than that of the model used above—you might check this for yourself. For more details, see the post at Bishop Hill:The fGn model has no trend.