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

We introduce Pairwise Distance-Diffusion Analysis (PDDA), a geometric framework that connects the Hurst exponent to the scaling of pairwise distances in long-memory stochastic processes. From a single distance-plot representation, PDDA yields three complementary routes to persistence: R/S-PDDA, base