Seasonal and Autoregressive Heteroskedasticity in the Central England Temperature Series

Abstract

We examine the temporal structure of the variance of residuals to a seasonal autoregressive model of the Central England Temperature. We find that the autocorrelation function of the squared residuals shows strong periodicity and that the residuals themselves are leptokurtotic, which we demonstrate by fitting a Student-t distribution to binned data. We fit a stationary seasonal heteroskedastic model to the series and also a GARCH(1,1) model. Using this heteroskedastic model, the kurtosis of the residuals are controlled and the residuals may be represented with a normal distribution. From the stationary seasonal heteroskedastic component of the model we infer that the variance of the temperature (January) is approximately four times that of the temperature (August). From the autoregressive character of the hetereoskedasticity we infer that naive relative coldness (this winter versus last winter) or relative hotness (this summer versus last summer) comparisons are likely prone to more error, in the form of a temporal localization bias, than popularly supposed.