  We introduce a generalization of Higuchi's estimator of the fractal dimension
as a new way to characterize the multifractal spectrum of univariate time
series. The resulting multifractal Higuchi dimension analysis (MF-HDA) method
considers the order-$q$ moments of the partition function provided by the
length of the time series graph at different levels of subsampling. The results
obtained for different types of stochastic processes as well as real-world
examples of word length series from fictional texts demonstrate that MF-HDA
provides a reliable estimate of the multifractal spectrum already for moderate
time series lengths. Practical advantages as well as disadvantages of the new
approach as compared to other state-of-the-art methods of multifractal analysis
are discussed, highlighting the particular potentials of MF-HDA to distinguish
mono- from multi-fractal dynamics based on relatively short time series.
