  Many studies on biological and soft matter systems report the joint presence
of a linear mean-squared displacement and a non-Gaussian probability density
exhibiting, for instance, exponential or stretched-Gaussian tails. This
phenomenon is ascribed to the heterogeneity of the medium and is captured by
random parameter models such as "superstatistics" or "diffusing diffusivity".
Independently, scientists working in the area of time series analysis and
statistics have studied a class of discrete-time processes with similar
properties, namely, random coefficient autoregressive models. In this work we
try to reconcile these two approaches and thus provide a bridge between
physical stochastic processes and autoregressive models. We start from the
basic Langevin equation of motion with time-varying damping or diffusion
coefficients and establish the link to random coefficient autoregressive
processes. By exploring that link we gain access to efficient statistical
methods which can help to identify data exhibiting Brownian yet non-Gaussian
diffusion.
