Slow convergence due to long range temporal correlations : models, phenomena, data analysis challenges.
Long range temporal correlations (LRC), i.e., an infinite correlation time, seems to be abundant in natural signals, such as climatological and physiological time series.
We discuss how to verify and quantify the presence of such correlations and show the limitations of the methods.
We highlight some statistical problems as a consequence of the presence of LRC such as bad convergence properties of time averages.
Lastly, we speculate about potential sources of LRC.