Abstract
In this paper we show fractional autoregressive integrated moving average (FARIMA) timeseries with a negative memory parameter and stable non-Gaussian noise model movementsof mRNA molecules inside live E. coli cells recorded by means of a single particle tracingexperiment. The phenomenon of negative memory is related to the so-called subdiffusionwhich is often observed in crowded media. We fit the FARIMA process by using a variantof Whittle’s method introduced by Kokoszka and Taqqu (1996 Ann. Statist. 24 1880) for theFARIMA stable case with a positive memory parameter, which we extend to the negativememory case. In order to show the goodness of fit we analyze residuals of themodel. We check that they follow a non-Gaussian stable law and justify theirindependence. Finally, with the help of Monte Carlo simulations, we illustrate that thefitted FARIMA model reproduces statistical properties of the analyzed biophysicaldata.
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