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OPTIMIZATION OF THE HIGUCHI METHOD
Author(s) -
J. A. Wanliss,
Ricardo Hernandez Arriaza,
Grace E Wanliss,
Steven I. Gordon
Publication year - 2021
Publication title -
international journal of research - granthaalayah
Language(s) - English
Resource type - Journals
eISSN - 2394-3629
pISSN - 2350-0530
DOI - 10.29121/granthaalayah.v9.i11.2021.4393
Subject(s) - fractional brownian motion , monte carlo method , fractal dimension , range (aeronautics) , fractal , dimension (graph theory) , series (stratigraphy) , expression (computer science) , a priori and a posteriori , computer science , hurst exponent , mathematics , set (abstract data type) , statistical physics , algorithm , brownian motion , mathematical optimization , statistics , mathematical analysis , physics , materials science , paleontology , programming language , philosophy , epistemology , pure mathematics , composite material , biology
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.

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