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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.08821 |
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| _version_ | 1866908263168081920 |
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| author | Nasr, Wejdene Ben Halconruy, Hélène Jaffard, Stéphane |
| author_facet | Nasr, Wejdene Ben Halconruy, Hélène Jaffard, Stéphane |
| contents | The motivation of this article is to estimate multifractality classification and model selection parameters: the first-order scaling exponent $c_1$ and the second-order 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Questioning Normality: A study of wavelet leaders distribution Nasr, Wejdene Ben Halconruy, Hélène Jaffard, Stéphane Applications Methodology The motivation of this article is to estimate multifractality classification and model selection parameters: the first-order scaling exponent $c_1$ and the second-order 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. |
| title | Questioning Normality: A study of wavelet leaders distribution |
| topic | Applications Methodology |
| url | https://arxiv.org/abs/2503.08821 |