  In the present study, we investigate the multifractal nature of a
long-cadence time series observed by the \textit{Kepler} mission for a sample
of 34 M dwarf stars and the Sun in its active phase. Using the Multifractal
Detrending Moving Average algorithm (MFDMA), which enables the detection of
multifractality in nonstationary time series, we define a set of multifractal
indices based on the multifractal spectrum profile as a measure of the level of
stellar magnetic activity. This set of indices is given by the ($A$,$\Delta
\alpha$,$C$,$H$)-quartet, where $A$, $\Delta \alpha$ and $C$ are related to
geometric features from the multifractal spectrum and the global Hurst exponent
$H$ describes the global structure and memorability of time series dynamics. As
a test, we measure these indices and compare them with a magnetic index defined
as $S_{ph}$ and verify the degree of correlation among them. First, we apply
the Poincar\'e plot method and find a strong correlation between the
$\left\langle S_{ph}\right\rangle$ index and one of the descriptors that
emerges from this method. As a result, we find that this index is strongly
correlated with long-term features of the signal. From the multifractal
perspective, the $\left\langle S_{ph}\right\rangle$ index is also strongly
linked to the geometric properties of the multifractal spectrum except for the
$H$ index. Furthermore, our results emphasize that the rotation period of stars
is scaled by the $H$ index, which is consistent with Skumanich's relationship.
Finally, our approach suggests that the $H$ index may be related to the
evolution of stellar angular momentum and a star's magnetic properties.
