Cyclical long-range dependence and the warming effect in a long temperature time series

In this paper, we propose a new approach for modelling a long temperature time series, using fractional cyclical integration. This model is based on the observation that the estimated spectrum of the series (the average annual temperature in Central England, 1659-2001) has its highest value at a frequency which is not zero, thus suggesting the existence of cycles at other frequencies. The results based on a fractional cyclical model show that there is a significant warming effect throughout the sample of about 0.22 degrees C/century. However, if we concentrate exclusively on the data corresponding to the 20th century that value increases to 0.64%. Moreover, the results in the paper show that a fractionally cyclically integrated model can be a competing alternative to other approaches based on fractional integration at the zero frequency. Copyright (C) 2007 Royal Meteorological Society.