Autoregressive conditional heteroscedasticity in daily temperature measurements

It is argued that the predictability of meteorological variables is not constant but shows regular variations. This is shown for the daily mean summer and winter temperatures at De Bilt, The Netherlands, over the last 30 years. To capture this feature, a generalized autoregressive conditional heteroscedastic (GARCH) model is proposed. In this model, the conditional variance of an observation depends linearly on the conditional variances of the previous observations and on the previous prediction errors. Here a GARCH(1,1) model is used for both the conditional variance and the conditional standard deviation, in conjunction with an AR(2) model for the mean, and conditionally normal errors. It is shown that these heteroscedastic models outperform their homoscedastic versions, and that the model which updates the conditional standard deviation is preferred.