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When observations are curves over some natural time interval, the field offunctional data analysis comes into play. Functional linear processes accountfor temporal dependence in the data. The prediction problem for functionallinear processes has been solved theoretically, but the focus for applicationshas been on functional autoregressive processes. We propose a newcomputationally tractable linear predictor for functional linear processes. Itis based on an application of the Multivariate Innovations Algorithm tofinite-dimensional subprocesses of increasing dimension of theinfinite-dimensional functional linear process. We investigate the behavior ofthe predictor for increasing sample size. We show that, depending on the decayrate of the eigenvalues of the covariance and the spectral density operator,the resulting predictor converges with a certain rate to the theoretically bestlinear predictor.

An Innovations Algorithm for the prediction of functional linear processes