Analysis of short subdiffusive time series: scatter of the time-averaged mean-squared displacement

We analyse the statistical behaviour of short time series in systems performing subdiffusion. Comparing the non-ergodic continuous time random walk model to the ergodic fractional Brownian motion, we demonstrate that the scatter between individual trajectories is not purely dominated by finite sample size effects but preserves some of the characteristics of the individual processes. In particular we show that the distribution of the time-averaged mean-squared displacements allows one to clearly distinguish between the two stochastic mechanisms even for a very short time series.