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Long-term observations have shown that black hole X-ray binaries exhibit strong, aperiodic variability on time-scales of a few milliseconds to seconds. The observed light curves display various characteristic features like a log-normal distribution of flux and a linear rms-flux relation, which indicate that the underlying variability process is stochastic in nature. It is also thought to be intrinsic to accretion. This variability has been modelled as inward propagating fluctuations of mass accretion rate, although the physical process driving the fluctuations remains puzzling. In this work, we analyse five exceptionally long duration general relativistic magnetohydrodynamic (GRMHD) simulations of optically thin, geometrically thick, black hole accretion flows to look for hints of propagating fluctuations in the simulation data. We find that the accretion profiles from these simulations do show evidence for inward propagating fluctuations below the viscous frequency by featuring strong radial coherence and positive time lags when comparing smaller to larger radii, although these time lags are generally shorter than the viscous time-scale and frequency independent. Our simulations also support the notion that the fluctuations in $\dot{M}$ build up in a multiplicative manner, as the simulations exhibit linear rms-mass flux relations, as well as log-normal distributions of their mass fluxes. When combining the mass fluxes from the simulations with an assumed emissivity profile, we additionally find broad agreement with observed power spectra and time lags, including a recovery of the frequency dependency of the time lags.