# Asymptotics for Spherical Functional Autoregressions

## TL;DR

This paper studies spherical functional autoregressive processes, establishing consistency, a central limit theorem, and weak convergence results for their estimation, supported by numerical validation.

## Contribution

It introduces new asymptotic results for spherical functional autoregressions, including consistency and limit theorems, under specific regularity conditions.

## Key findings

- Established consistency in sup and mean-square norms
- Proved a quantitative central limit theorem in Wasserstein distance
- Validated results with numerical experiments

## Abstract

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 sup and mean-square 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.