标题： 几何泛函的分数协整 显示英文标题

标题： Fractional Cointegration of Geometric Functionals

摘要： 在本文中，我们表明在球面-时间长记忆随机场的超越集上评估的几何泛函（例如，超越区域、边界长度）可以表现出分数协整，这意味着它们的一些线性组合具有比原始向量更短的记忆性。 这些结果证明了在不同阈值处评估的泛函之间存在长期均衡关系；作为统计应用，我们讨论了Adler-Taylor度量因子的频域估计量，即场的梯度方差。 我们的结果也通过蒙特卡洛模拟进行了说明。 显示英文摘要

摘要： 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.