Abstract In this paper, we characterize multi-scaling dynamics by estimating the permutation entropy at different time lags. Numerical simulations generated from fractional Brownian motion were used to illustrate how this multiscale symbolic tool behaves at the crossovers between different scaling. Experimental applications were also analyzed to show the applicability of this approach in practical situations. We consider that our findings can be of help to reach a better understanding and interpretation of the results obtained when this entropic measure is implemented to analyze systems with scale-dependent dynamics.