Pairwise Distance-Diffusion Analysis (PDDA): A Geometric Framework for Estimating Hurst Exponents in Multivariate Long-Memory Processes

TL;DR

The paper presents PDDA, a geometric framework for estimating Hurst exponents in multivariate long-memory processes using distance plots, unifying classical methods and extending to multivariate cases.

Contribution

Introduces PDDA, a novel geometric approach that unifies and extends existing Hurst exponent estimation methods to multivariate long-memory processes.

Findings

PDDA provides two complementary estimation routes: R/S-PDDA and MSD-PDDA.

Extended PDDA to multivariate isotropic and anisotropic processes.

Derived explicit links between persistence, range dimension, and recurrence statistics.

Abstract

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.