  When observations are curves over some natural time interval, the field of
functional data analysis comes into play. Functional linear processes account
for temporal dependence in the data. The prediction problem for functional
linear processes has been solved theoretically, but the focus for applications
has been on functional autoregressive processes. We propose a new
computationally tractable linear predictor for functional linear processes. It
is based on an application of the Multivariate Innovations Algorithm to
finite-dimensional subprocesses of increasing dimension of the
infinite-dimensional functional linear process. We investigate the behavior of
the predictor for increasing sample size. We show that, depending on the decay
rate of the eigenvalues of the covariance and the spectral density operator,
the resulting predictor converges with a certain rate to the theoretically best
linear predictor.
