John Dagsvik: How Does the Temperature Vary over Time? Evidence on the Stationary and Fractal Nature of Temperature Fluctuations

Title:
How Does the Temperature Vary over Time?  
Evidence on the Stationary and Fractal  
Nature of Temperature Fluctuations
 
Abstract:
This paper analyses temperature time series  
data obtained from 95 worldwide weather stations,  
as well as reconstructed data from the last two  
millennia. We propose an empirical strategy  
based on three key invariance hypotheses. The  
first is that the temperature process is stationary.  
The second is that the distribution of the average  
temperature over any specific time period does not  
depend on the length of the period, apart from  
a scale transformation. The third is that the  
temperature process is Gaussian. These hypotheses  
imply that the temperature series follow a so-called
Fractional Gaussian Noise process, which is known  
to exhibit long range dependence. In order to test  
our hypotheses we have applied non-parametric graphical  
methods and Chi-square tests. The tests indicate  
that both the observed and the reconstructed data  
are consistent with the Fractional Gaussian Noise model.