We have explored and analyzed the outcome data from several simulated superstatistical time series including an $E^{\mu -1}$ density of states. Among the three main classes of superstatistics (SS), we have chosen the one that imposes a gamma distribution $g\left(\beta \right)$ for the fluctuating intensive parameter $\beta$. In our analysis, we have generated a set of synthetic time series through a simple algorithm, which provided us different dynamical scenarios by setting some relevant superstatistical parameters. In each emerging scenario, multifractal detrended fluctuation analysis (MFDFA) was applied to evaluate the corresponding singularity spectrum width $\mathrm{\Delta }\alpha$. With this information we have characterized the complexity' degree of each superstatistical time series. The results show that the complexity is strongly dependent on the shape parameter $\nu$ of $g\left(\beta \right)$ and that, in any of these cases, the parameter $\mu$ associated with the density of states smoothly increases said complexity. A multiple regression model shows that although $\mu$ and $\nu$ do not interact significantly, they do act complementary to describe the system's complexity as measured by $\mathrm{\Delta }\alpha$. This analysis confirms that the simulated data could represent the behavior of some complex systems whose complexity can be effectively described by the regression model through $\mu$ and $\nu$. This conclusion is further supported by the assessment of eight SYM-H magnitude datasets, taken during periods of maximum and minimum solar activity, where predicted $\mathrm{\Delta }\alpha$ values are reasonably close to the corresponding values obtained through the MFDFA.

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• Fractal analysis
• Nonequilibrium statistical mechanics
• Stochastic processes