  In the present study, high-precision time series photometry for the active
\emph{Kepler} stars is described in the language of multifractals. We explore
the potential of using the rescaled range analysis ($R/S$) and multifractal
detrended moving average analysis (MFDMA) methods to characterize the
multiscale structure of the observed time series from a sample of $\sim$40 000
active stars. Among these stars, 6486 have surface differential rotation
measurement, whereas 1846 have no signature of differential rotation. As a
result, the Hurst exponent ($H$) derived from both methods shows a strong
correlation with the period derived from rotational modulation. In addition,
the variability range $R_{var}$ reveals how this correlation follows a high
activity ``line''. We also verify that the $H$-index is an able parameter for
distinguishing the different signs of stellar rotation that can exist between
the stars with and without differential rotation. In summary, the results
indicate that the Hurst exponent is a promising index for estimating
photometric magnetic activity.

Solar and Stellar Astrophysics