Pairwise Distance-Diffusion Analysis (PDDA): A Geometric Framework for Estimating Hurst Exponents in Multivariate Long-Memory Processes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914584594481152 |
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| author | Soriano, Diogo C. Vanheusden, Frederique Nasuto, Slawomir J. |
| author_facet | Soriano, Diogo C. Vanheusden, Frederique Nasuto, Slawomir J. |
| contents | We introduce Pairwise Distance-Diffusion Analysis (PDDA), a geometric framework for estimating the Hurst exponent from distance plots of long-memory stochastic processes. A single construction yields two complementary routes: R/S-PDDA, a geometric reformulation of the classical rescaled-range definition, and MSD-PDDA, based on mean-squared-displacement scaling, classically used in anomalous diffusion. We extend PDDA to multivariate isotropic and anisotropic processes and derive an explicit link between temporal persistence, range dimension, and recurrence statistics, providing a unified distance-based foundation for Hurst analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_21530 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pairwise Distance-Diffusion Analysis (PDDA): A Geometric Framework for Estimating Hurst Exponents in Multivariate Long-Memory Processes Soriano, Diogo C. Vanheusden, Frederique Nasuto, Slawomir J. Methodology Chaotic Dynamics Data Analysis, Statistics and Probability We introduce Pairwise Distance-Diffusion Analysis (PDDA), a geometric framework for estimating the Hurst exponent from distance plots of long-memory stochastic processes. A single construction yields two complementary routes: R/S-PDDA, a geometric reformulation of the classical rescaled-range definition, and MSD-PDDA, based on mean-squared-displacement scaling, classically used in anomalous diffusion. We extend PDDA to multivariate isotropic and anisotropic processes and derive an explicit link between temporal persistence, range dimension, and recurrence statistics, providing a unified distance-based foundation for Hurst analysis. |
| title | Pairwise Distance-Diffusion Analysis (PDDA): A Geometric Framework for Estimating Hurst Exponents in Multivariate Long-Memory Processes |
| topic | Methodology Chaotic Dynamics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2605.21530 |