Fractional process as a unified model for subdiffusive dynamics in experimental data.

We show how to use a fractional autoregressive integrated moving average (FARIMA) model to a statistical analysis of the subdiffusive dynamics. The discrete time FARIMA(1,d,1) model is applied in this paper to the random motion of an individual fluorescently labeled mRNA molecule inside live E. coli cells in the experiment described in detail by Golding and Cox [Phys. Rev. Lett. 96, 098102 (2006)] as well as to the motion of fluorescently labeled telomeres in the nucleus of live human cells (U2OS cancer) in the experiment performed by Bronstein et al. [Phys. Rev. Lett. 103, 018102 (2009)]. It is found that only the memory parameter d of the FARIMA model completely detects an anomalous dynamics of the experimental data in both cases independently of the observed distribution of random noises.