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The stochastic trajectories of molecules in living cells, as well as thedynamics in many other complex systems, often exhibit memory in their path overlong periods of time. In addition, these systems can show dynamicheterogeneities due to which the motion changes along the trajectories. Sucheffects manifest themselves as spatiotemporal correlations. Despite the broadoccurrence of heterogeneous complex systems in nature, their analysis is stillquite poorly understood and tools to model them are largely missing. Wecontribute to tackling this problem by employing an integral representation ofMandelbrot's fractional Brownian motion that is compliant with varying motionparameters while maintaining long memory. Two types of switching fractionalBrownian motion are analysed, with transitions arising from a Markovianstochastic process and scale-free intermittent processes. We obtain simpleformulas for classical statistics of the processes, namely the mean squareddisplacement and the power spectral density. Further, a method to identifyswitching fractional Brownian motion based on the distribution of displacementsis described. A validation of the model is given for experimental measurementsof the motion of quantum dots in the cytoplasm of live mammalian cells thatwere obtained by single-particle tracking.

Modelling intermittent anomalous diffusion with switching fractional Brownian motion