Fractional Cointegration of Geometric Functionals
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915388737978368 |
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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 |