Open Access
August 2020 Frequency domain theory for functional time series: Variance decomposition and an invariance principle
Piotr Kokoszka, Neda Mohammadi Jouzdani
Bernoulli 26(3): 2383-2399 (August 2020). DOI: 10.3150/20-BEJ1199


This paper is concerned with frequency domain theory for functional time series, which are temporally dependent sequences of functions in a Hilbert space. We consider a variance decomposition, which is more suitable for such a data structure than the variance decomposition based on the Karhunen–Loéve expansion. The decomposition we study uses eigenvalues of spectral density operators, which are functional analogs of the spectral density of a stationary scalar time series. We propose estimators of the variance components and derive convergence rates for their mean square error as well as their asymptotic normality. The latter is derived from a frequency domain invariance principle for the estimators of the spectral density operators. This principle is established for a broad class of linear time series models. It is a main contribution of the paper.


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Piotr Kokoszka. Neda Mohammadi Jouzdani. "Frequency domain theory for functional time series: Variance decomposition and an invariance principle." Bernoulli 26 (3) 2383 - 2399, August 2020.


Received: 1 May 2019; Revised: 1 November 2019; Published: August 2020
First available in Project Euclid: 27 April 2020

zbMATH: 07193964
MathSciNet: MR4091113
Digital Object Identifier: 10.3150/20-BEJ1199

Keywords: functional data , invariance principle , spectral analysis , time series , variance decomposition

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 3 • August 2020
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