Pré-Publication, Document De Travail Année : 2025

Questioning normality: a study of wavelet leaders distribution

Résumé

The motivation of this article is to estimate multifractality classification and model selection parameters : the first-order scaling exponent c 1 and the secondorder scaling exponent (or intermittency coefficient) c 2 . These exponents are built on wavelet leaders, which therefore constitute fundamental tools in applied multifractal analysis. While most estimation methods, particularly Bayesian approaches, rely on the assumption of log-normality, we challenge this hypothesis by statistically testing the normality of log-leaders. Upon rejecting this common assumption, we propose instead a novel model based on log-concave distributions. We validate this new model on well-known stochastic processes, including fractional Brownian motion, the multifractal random walk, and the canonical Mandelbrot cascade, as well as on real-world marathon runner data. Furthermore, we revisit the estimation procedure for c 1 , providing confidence intervals, and for c 2 , applying it to fractional Brownian motions with various Hurst indices as well as to the multifractal random walk. Finally, we establish several theoretical results on the distribution of log-leaders in random wavelet series, which are consistent with our numerical findings.

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Dates et versions

hal-04987183 , version 1 (11-03-2025)

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  • HAL Id : hal-04987183 , version 1

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Hélène Halconruy, Stéphane Jaffard, Wejdene Nasr Ben Hadj Amor. Questioning normality: a study of wavelet leaders distribution. 2025. ⟨hal-04987183⟩
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