{"ID":2894831,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.10184","arxiv_id":"2507.10184","title":"Fractional Cointegration of Geometric Functionals","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.","short_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...","url_abs":"https://arxiv.org/abs/2507.10184","url_pdf":"https://arxiv.org/pdf/2507.10184v1","authors":"[\"Alessia Caponera\",\"Domenico Marinucci\",\"Anna Vidotto\"]","published":"2025-07-14T11:50:04Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}