The Accuracy of Autoregressive Forecasts of the Average Monthly Temperatures in Central England, Central Park and New Jersey

Abstract

The corrected Akaike Information Criterion (AICc) is used to chose order of the best approximating model to the pre-industrial revolution era data (January, 1659, to December, 1849; 2292 observations) for the Central England Temperature, parameterized as a standard Box-Jenkins style autoregressive and seasonally-autoregressive model with a linear trend component. The result is an AR(5) SAR(29) model that incorporates the complex seasonality, tempo- ral and secular trends of the average monthly temperature and, as a forecasting model of future temperature, performs well out-of-sample. Fixing the order and the coefficients of the discovered model, it is then used to forecast three datasets commencing with the beginning of the Second Industrial Revolution period and ending at the end of the 20th. Century (January, 1850, to December, 1999; 1572 observations). Those data sets are the Central England temperature; the Average New Jersey temperature and the Central Park temper- ature. The systematic geographic variation in the temperatures between the sites considered is modelled via a simple linear transformation of the forecasts made for the Central England data. The observed accuracy of the transformed fore- casts validate the structural form of the complex autoregressive model on smaller data sets and also validates the modeling of regional temperature variations as a combination of a global factor and an local idiosyncratic variation. Subsequently the full model, with the autoregressive orders fixed but the pa- rameters free to vary, is separately fitted to each industrial era data set. Although all three series show an upward trend in temperature during this period, and that of the New York City data is higher than the other pair and by itself statistically distinct from zero, there is no significant evidence from this analysis to support the hypothesis that trend rates individually estimated for the three series are in- consistent with each other. It is further demonstrated that the autocorrelative lag coefficients discovered by regression analysis are consistent with those derived from the larger pre-industrial era data set after the effect of imprecision in their estimation is accounted for. Finally, both the linearly transformed forecasts of the Central England data and the fitted Industrial Era models are used to forecast their respective series in the 21st. Century.