  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.
