  This paper addresses the prediction of stationary functional time series.
Existing contributions to this problem have largely focused on the special case
of first-order functional autoregressive processes because of their technical
tractability and the current lack of advanced functional time series
methodology. It is shown here how standard multivariate prediction techniques
can be utilized in this context. The connection between functional and
multivariate predictions is made precise for the important case of vector and
functional autoregressions. The proposed method is easy to implement, making
use of existing statistical software packages, and may therefore be attractive
to a broader, possibly non-academic, audience. Its practical applicability is
enhanced through the introduction of a novel functional final prediction error
model selection criterion that allows for an automatic determination of the lag
structure and the dimensionality of the model. The usefulness of the proposed
methodology is demonstrated in a simulation study and an application to
environmental data, namely the prediction of daily pollution curves describing
the concentration of particulate matter in ambient air. It is found that the
proposed prediction method often significantly outperforms existing methods.
