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

Jesús A. Sosa-Herrera and Suemi Rodríguez-Romo

Physica A: Statistical Mechanics and its Applications, 2019, vol. 526, issue C

Abstract: MF-DFA is a widely used method for the extraction of multifractal patterns that may appear in time series. Current techniques for determining the range of scales employed in the MF-DFA procedure are mainly empirical and in some cases require the researcher to visually select such range, so multifractal measures often differ among experiments, and the estimation of errors in such measures is often disregarded. This problem also represents a serious obstacle for incorporating MF-DFA in automated processes. In this paper, we present a Kernel Density based method that provides metrics for errors on the estimations of the multifractal spectrum obtained by MF-DFA, and gives the probabilities of errors being inside a certain range for each moment considered in the spectrum. Our approach makes use of Kernel Density Estimation in combination with a variant of the Theil–Sen estimator to compute MF-DFA exponents. We tested our technique on simulated and real-world time series. Comparison between this approach and the conventional method applied to deterministic and random multiplicative processes demonstrates robustness to spurious estimations of generalized fractal dimensions in MF-DFA.

Keywords: Regression; Multifractals; Time series (search for similar items in EconPapers)
Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437119304716
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:526:y:2019:i:c:s0378437119304716

DOI: 10.1016/j.physa.2019.04.099

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().