Generalization of Higuchi’s fractal dimension for multifractal analysis of time series with limited length

There exist several methodologies for the multifractal characterization of nonstationary time series. However, when applied to sequences limited length, these methods often tend overestimate actual properties. To address this aspect, we introduce here a generalization Higuchi’s estimator fractal dimension as new way characterize spectrum univariate series or relatively short length. This Higuchi analysis (MF-HDA) method considers order-q moments partition function provided by length graph at different levels subsampling. The results obtained types stochastic processes, classical model, and various real-world examples word from fictional texts demonstrate that MF-HDA provides reliable estimate already moderate lengths. Practical advantages well disadvantages approach compared other state-of-the-art are discussed, highlighting particular potentials distinguish mono- dynamics based on sequences.