In this paper, we investigate a class of spherical functional autoregressive processes, and we discuss the estimation of the corresponding autoregressive kernels. In particular, we first establish a consistency result (in mean-square and sup norm), then a quantitative central limit theorem (in Wasserstein distance), and finally a weak convergence result, under more restrictive regularity conditions. Our results are validated by a small numerical investigation.

中文翻译：

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球形函数自回归的渐近性

在本文中，我们研究了一类球面函数自回归过程，并讨论了相应自回归核的估计。特别是，我们首先建立一致性结果（均方和最高范数），然后建立定量中心极限定理（以Wasserstein距离为单位），最后在更严格的规则性条件下建立弱收敛结果。我们的结果通过一个小的数值研究得到了验证。