Continued musings on the time-series analysis of the Central England Temperature series have lead me to look at processes for the variance of the temperature. I found seasonal heteroskedasticity, which i don't regard as suprising, and autoregressive heteroskedasticity — i.e. GARCH — which I do think is kind of interesting. It means that the climatic process that generates our weather can undergo “bursts” of volatility that persist for a while and then ebb away. So an anomalously hot month is just as likely to be followed by either an another anomalously hot month or an anomalously cold month but less likely to be followed by a normal month. Perhaps this is what makes the weather so confusing!

Anyway, p-Value laden statistical analysis is available at the SSRN

I recently wrote up, and submitted to the Social Science Research Network, a study of the Central England Temperature series that I did a couple of years ago and recently updated. You can access the paper at the SSRN here: A Seasonal Autoregressive Model for the Central England Temperature Series.

What I do in this analysis is build a seasonal autoregressive model for what is the longest time series of directly measured temperatures available for analysis. This model includes a linear trend component. I fit the model for both the pre-Industrial Revolution Period (1659 to 1849) and the Post-Industrial Revolution period (1949 to 1999). In the former period no trend is apparent, in the latter period I find a warming trend of 1 °C/century. This result has a borderline statistical significance (less than 3σ). I use both models to forecast the temperatures for the 21st. Century and find that the older, trend free, model does a slightly better job out-of-sample than the newer model with the trend.