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arXiv · 2507.10184

Fractional Cointegration of Geometric Functionals

Alessia Caponera·Domenico Marinucci·Anna Vidotto
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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.

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Alessia Caponera, Domenico Marinucci, Anna Vidotto. 2025-07-14. Fractional Cointegration of Geometric Functionals. https://arxiv.org/abs/2507.10184

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