TRENDs in Distributional Characteristics: Existence of Global Warming

We define Global Warming (GW) as the existence of a trend in a given characteristic of the temperature distribution, not only in the mean. These new trends are characterized following the suggestions in Granger and White (2011). In order to make the new concept operational we propose to estimate the distributional characteristics (Ci) by realized quantiles (RQ). In this way, they are converted into time series objects and we can apply all the time series analysis tools. The paper proposes a robust “low-cost econometrics” test for the existence of an unknown trend in a given characteristic (null hypothesis is notrend). Asymptotic properties of the test as well as its finite sample performance are provided. For those characteristics where the null is rejected, we model and estimate their trend behavior. Different trend models are specified (via general to particular significance testing and model selection criteria) and a forecasting competition is run. Forecasting evaluation tests are used to choose the best trend model for Cit. With these trend models, we are able to produce forecasts of the trending behavior of temperature distribution and not only of the mean as it is the standard procedure in this literature. This paper applies this novelty approach to study the existence of GW (regional warming) in the center of UK, 1772-2012 thermometer data, to conclude that GW is more on the lower quartiles of the temperature distribution than in the upper part. These results are also maintained in other northern hemisphere places like Stockholm, Cadiz and Milan.