Kernel density approach to error estimation of MF-DFA measures on time series

Sosa-Herrera, Jesús A.; Rodríguez‐Romo, Suemi

doi:10.1016/j.physa.2019.04.099

Cited by 2 publications

(1 citation statement)

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“…Lavicka et al [25] analyzed the electric power load time series of 35 independent countries and improved the basic MF-DFA with unified shuffling and substitution of the dataset to prove the robustness of the results to nonlinear effects. Sosa-Herrera et al [26] proposed a method based on kernel density that provides an error index for estimation of the multi-fractal spectrum obtained by MF-DFA, and gave the probability of error within a certain range at each moment in the spectrum. Comparison between this method and the traditional methods applied to deterministic and random multiplication processes proved the robustness of false estimation of generalized fractals in MF-DFA.…”

Section: Introductionmentioning

confidence: 99%

Sign Retention in Classical MF-DFA

2022

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In this paper, we propose a one-dimensional (1D) multifractal sign retention detrending fluctuation analysis algorithm (MF-S-DFA). The proposed method is based on conventional multifractal detrending fluctuation analysis (MF-DFA). As negative values may exist in the calculation in the original MF-DFA model, sign retention is considered to improve performance. We evaluate the two methods based on time series constructed by p-model multiplication cascades. The results indicate that the generalized Hurst exponent H(q), the scale exponent τ(q) and the singular spectrum f(α) estimated by MF-S-DFA behave almost consistently with the theoretical values. Moreover, we also employ distance functions such as DH and Dτ. The results prove that MF-S-DFA achieves more accurate estimation. In addition, we present various numerical experiments by transforming parameters such as nmax, q and p. The results imply that MF-S-DFA obtains more excellent performance than that of conventional MF-DFA in all cases. Finally, we also verify the high feasibility of MF-S-DFA in ECG signal classification. Through classification of normal and abnormal ECG signals, we further corroborate that MF-S-DFA is more effective than conventional MF-DFA.

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Section: Introductionmentioning

confidence: 99%