A Seasonal Autoregressive Model for the Central England Temperature Series

Abstract

We propose a simple seasonal autoregressive model with a linear trend to forecast the Central England Temperature record. The data is divided into three distinct epochs: pre-industrial revolution, post-industrial revolution, and 21st. Century. An AR(3)xSAR(8) seasonal autoregressive model with linear trend is identified as describing the data for the pre-I.R. period. That model structure is estimated independently on the post-I.R. data. We compare the functional forms of the models and their relative skill in forecasting the temperature during the 21st. Century, during which time both models are out-of-sample. We find that the post-I.R. model possesses a warming trend at a borderline level of statistical significance (2.6 sigma). However, the pre-I.R. model without the warming trend does a better job of forecasting the 21st. Century temperature record than the post-I.R. model.