Fractional Cointegration of Geometric Functionals
Probability
2025-07-15 v1 Statistics Theory
Statistics Theory
Abstract
In this paper, we show that geometric functionals (e.g., excursion area, boundary length) evaluated on excursion sets of sphere-cross-time long memory random fields can exhibit fractional cointegration, meaning that some of their linear combinations have shorter memory than the original vector. These results prove the existence of long-run equilibrium relationships between functionals evaluated at different threshold values; as a statistical application, we discuss a frequency-domain estimator for the Adler-Taylor metric factor, i.e., the variance of the field's gradient. Our results are illustrated also by Monte Carlo simulations.
Cite
@article{arxiv.2507.10184,
title = {Fractional Cointegration of Geometric Functionals},
author = {Alessia Caponera and Domenico Marinucci and Anna Vidotto},
journal= {arXiv preprint arXiv:2507.10184},
year = {2025}
}