Fractional Cointegration of Geometric Functionals

Fuente: arXiv
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Main Authors: Caponera, Alessia, Marinucci, Domenico, Vidotto, Anna
Format: Preprint
Published: 2025
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author Caponera, Alessia
Marinucci, Domenico
Vidotto, Anna
author_facet Caponera, Alessia
Marinucci, Domenico
Vidotto, Anna
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_10184
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Fractional Cointegration of Geometric Functionals
Caponera, Alessia
Marinucci, Domenico
Vidotto, Anna
Probability
Statistics Theory
60G60, 62M10, 62M15, 62M40
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.
title Fractional Cointegration of Geometric Functionals
topic Probability
Statistics Theory
60G60, 62M10, 62M15, 62M40
url https://arxiv.org/abs/2507.10184