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Multifractal surrogate-data generation algorithm that preserves pointwise Hölder regularity structure, with initial applications to turbulence
Version 2 2021-01-08, 11:58
Version 1 2018-05-15, 12:50
journal contributionposted on 2021-01-08, 11:58 authored by Chris KeylockChris Keylock
An algorithm is described that can generate random variants of a time series while preserving the probability distribution of original values and the pointwise Hoelder regularity. Thus, it preserves the multifractal properties of the data. Our algorithm is similar in principle to well-known algorithms based on the preservation of the Fourier amplitude spectrum and original values of a time series. However, it is underpinned by a dual-tree complex wavelet transform rather than a Fourier transform. Our method, which we term the iterated amplitude adjusted wavelet transform can be used to generate bootstrapped versions of multifractal data, and because it preserves the pointwise Hoelder regularity but not the local Hoelder regularity, it can be used to test hypotheses concerning the presence of oscillating singularities in a time series, an important feature of turbulence and econophysics data. Because the locations of the data values are randomized with respect to the multifractal structure, hypotheses about their mutual coupling can be tested, which is important for the velocity-intermittency structure of turbulence and self-regulating processes.
This work was supported by NERC Grant No. NE/F00415X/1, EPSRC Grant No. EP/K007688/1, and Royal Academy of Engineering/Leverhulme Senior Research Fellowship LTSRF1516-12-89.
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Published inPhysical Review E
CitationKEYLOCK, C.J., 2017. Multifractal surrogate-data generation algorithm that preserves pointwise Hoelder regularity structure, with initial applications to turbulence. Physical Review E, 95 (3), 032123.
Publisher© American Physical Society
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis paper was published in the journal Physical Review E and the definitive published version is available at https://doi.org/10.1103/PhysRevE.95.032123.