Ergodicity breakdown and scaling from single sequences

In the ergodic regime, several methods efficiently estimate the temporal scaling of time series characterized by long-range power-law correlations by converting them into diffusion processes. However, in the condition of ergodicity breakdown, the same methods give ambiguous results. We show that in such regime, two different scaling behaviors emerge depending on the age of the windows used for the estimation. We explain the ambiguity of the estimation methods by the different influence of the two scaling behaviors on each method. Our results suggest that aging drastically alters the scaling properties of non-ergodic processes.