How does temperature vary over time?: evidence on the stationary and fractal nature of temperature fluctuations

Abstract

The paper analyses temperature data from 96 selected weather stations world wide, and from reconstructed northern hemisphere temperature data over the last two millennia. Using a non-parametric test, we find that the stationarity hypothesis is not rejected by the data. Subsequently, we investigate further properties of the data by means of a statistical model known as the fractional Gaussian noise (FGN) model. Under stationarity FGN follows from the fact that the observed data are obtained as temporal aggregates of data generated at a finer (basic) timescale where temporal aggregation is taken over a ‘large’ number of basic units. The FGN process exhibits long-range dependence. Several tests show that both the reconstructed and most of the observed data are consistent with the FGN model.