# A review and comparative study on functional time series techniques

## TL;DR

This paper reviews estimation, prediction, and testing methods for functional time series in Hilbert and Banach spaces, comparing ARH(1) approaches through simulations to evaluate their effectiveness.

## Contribution

It provides a comprehensive review and comparison of parametric and non-parametric methods for ARH(1) processes in functional data analysis.

## Key findings

- Different ARH(1) prediction methods are compared via simulations.
- Estimation and prediction results are summarized for functional time series.
- Statistical tests are discussed in both parametric and non-parametric frameworks.

## Abstract

This paper reviews the main estimation and prediction results derived in the context of functional time series, when Hilbert and Banach spaces are considered, specially, in the context of autoregressive processes of order one (ARH(1) and ARB(1) processes, for H and B being a Hilbert and Banach space, respectively). Particularly, we pay attention to the estimation and prediction results, and statistical tests, derived in both parametric and non-parametric frameworks. A comparative study between different ARH(1) prediction approaches is developed in the simulation study undertaken.