An innovations algorithm for the prediction of functional linear processes

J. Klepsch, C. Klüppelberg

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish
Pages (from-to)252-271
Number of pages20
JournalJournal of Multivariate Analysis
StatePublished - 1 Mar 2017


  • Functional data analysis (FDA)
  • Functional linear process
  • Functional principal components
  • Functional time series
  • Hilbert space valued process
  • Innovations Algorithm
  • Prediction
  • Prediction error


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