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The performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono- and multifractal models. The reconstruction of the generalized Hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of the decreasing length of the series. As an application the series of the daily exchange rate between the U.S. dollar and the euro is studied.
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based mul
Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy, heterogeneous and exhibit different types of nonstationarities, which c
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling relation over
We describe an algorithm for simulating ultrasound propagation in random one-dimensional media, mimicking different microstructures by choosing physical properties such as domain sizes and mass densities from probability distributions. By combining a
We introduce a generalization of Higuchis 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-$