Fractional Cointegration of Geometric Functionals

2025/07/14 by Alessia Caponera, Caponera, Alessia, Domenico Marinucci +3
Mathematics · #60G60 #62M10 #62M15 #62M40 #FOS: Mathematics #Functional Equations Stability Results #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Analysis #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2507.10184

openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• LRD spectral analysis of multifractional functional time series on manifolds
• Fluctuations of Level Curves for Time-Dependent Spherical Random Fields
• Rudin Extension Theorems on Product Spaces, Turning Bands, and Random Fields on Balls cross Time
• Sojourn functionals for spatiotemporal random fields with long-memory
• SPHARMA approximations for stationary functional time series on the sphere
• LASSO estimation for spherical autoregressive processes
• Asymptotics for Spherical Functional Autoregressions
• Identifying Cointegration by Eigenanalysis
• Semiparametric estimation of fractional cointegrating subspaces

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