An Innovations Algorithm for the prediction of functional linear processes

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 applic...

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Bibliographic Details
Published in:arXiv.org 2016-07
Main Authors: Klepsch, Johannes, Klüppelberg, Claudia
Format: Article
Language:English
Subjects:
Algorithms
Autoregressive processes
Covariance
Data analysis
Decay rate
Dependence
Eigenvalues
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1607.05874