On the CLT for discrete Fourier transforms of functional time series

Cerovecki, Clément; Hörmann, Siegfried

doi:10.48550/arxiv.1506.00970

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2017

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“…Theorem 1 and 4 of [9] infer the following duality between C X;h and F X [ω], with A[z] as in (6.5) and adjoint A[z] * :…”

Section: Proofsmentioning

confidence: 99%

An innovations algorithm for the prediction of functional linear processes

Klepsch

Klüppelberg

2017

Journal of Multivariate Analysis

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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.

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“…Theorem 1 and 4 of [9] infer the following duality between C X;h and F X [ω], with A[z] as in (6.5) and adjoint A[z] * :…”

Section: Proofsmentioning

confidence: 99%