论文标题
球体上固定功能时间序列的司伐近似
SPHARMA approximations for stationary functional time series on the sphere
论文作者
论文摘要
在本文中，我们专注于各向同性和固定球体 - 交叉的随机场。我们首先介绍了球形功能自动回旋运动平均过程（SPHARMA）的类别，该过程以自然的方式扩展了[8，7]中最近研究的球形功能自动化（SPHAR）；更重要的是，我们表明，可以利用足够大阶的SPHAR和SPHARMA过程，以近似于每个各向同性和固定的球体 - 跨时间随机场，从而将其推广到该无限二二维框架上的一些经典结果，以实现真实价值的平稳过程。还建立了从功能频谱表示定理和Wold样分解方面的进一步表征。
In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressions (SPHAR) recently studied in [8, 7]; more importantly, we then show that SPHAR and SPHARMA processes of sufficiently large order can be exploited to approximate every isotropic and stationary sphere-cross-time random field, thus generalizing to this infinite-dimensional framework some classical results on real-valued stationary processes. Further characterizations in terms of functional spectral representation theorems and Wold-like decompositions are also established.
