Abstract
Background and Objective: Higuchi’s method of determining fractal dimension (HFD) occupies a valuable place in the study of a wide variety of physical signals. In comparison to other methods, it provides more rapid, accurate estimations for the entire range of possible fractal dimensions. However, a major difficulty in using the method is the correct choice of tuning parameter (kmax) to compute the most accurate results. In the past researchers have used various ad hoc methods to determine the appropriate kmax choice for their particular data. We provide a more objective method of determining, a priori, the best value for the tuning parameter, given a particular length data set. Methods: We create numerous simulations of fractional Brownian motion to perform Monte Carlo simulations of the distribution of the calculated HFD. Results: Experimental results show that HFD depends not only on kmax but also on the length of the time series, which enable derivation of an expression to find the appropriate kmax for an input time series of unknown fractal dimension. Conclusion: The Higuchi method should not be used indiscriminately without reference to the type of data whose fractal dimension is examined. Monte Carlo simulations with different fractional Brownian motions increases the confidence of evaluation results.
Highlights
The Higuchi algorithm Higuchi (1988) is one of many widely used methods to compute fractal properties of complex nonlinear physical signals Esteller et al (2001)
Experimental results show that Higuchi fractal dimension (HFD) depends on kmax and on the length of the time series, which enable derivation of an expression to find the appropriate kmax for an input time series of unknown fractal dimension
We call the fractal dimension calculated via the Higuchi algorithm the Higuchi fractal dimension (HFD)
Summary
The Higuchi algorithm Higuchi (1988) is one of many widely used methods to compute fractal properties of complex nonlinear physical signals Esteller et al (2001). It is often preferred when big data are analyzed because it is stable, rapid, accurate, relatively low-cost, and excels better known linear methods. Higuchi’s method of determining fractal dimension (HFD) occupies a valuable place in the study of a wide variety of physical signals. Methods: We create numerous simulations of fractional Brownian motion to perform Monte Carlo simulations of the distribution of the calculated HFD. Monte Carlo simulations with different fractional Brownian motions increases the confidence of evaluation results
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