Focus regression for multifractal analysis

Wolfgang Schadner

Chaos, Solitons & Fractals, 2026, vol. 209, issue P1

Abstract: We propose a regression framework to estimate a time-series’ generalized Hurst exponents in a consistent way while reducing systematic errors, ensuring valid singularity spectra. The method serves as a robustness enhancement for popular approaches like de-trended fluctuation analysis and wavelet leaders. Given moment-scaling functions across scales and moments, the idea is to enforce all regression lines to pass through a common point of intersection, called the focus. Unlike the existing literature, we treat the focus position as a free parameter, yielding better fits and reduced distortion in estimated multifractality. We derive explicit least-squares solutions, including the globally optimal focus position. Simulations and an empirical finance application demonstrate practical relevance of this work.

Keywords: Common point regression; Singularity spectrum; MF-DFA; Hurst exponent; Fractal analysis; Power-law scaling (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926005096

DOI: 10.1016/j.chaos.2026.118368

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