The Maximum of the Periodogram of a Sequence of Functional Data

Clément Cerovecki, Vaidotas Characiejus and Siegfried Hörmann

Journal of the American Statistical Association, 2023, vol. 118, issue 544, 2712-2720

Abstract: We study the periodogram operator of a sequence of functional data. Using recent advances in Gaussian approximation theory, we derive the asymptotic distribution of the maximum norm over all fundamental frequencies. We consider the case where the noise variables are independent and then generalize our results to functional linear processes. Our theory can be used for detecting periodic signals in functional time series when the length of the period is unknown. We demonstrate the proposed methodology in a simulation study as well as on real data. Supplementary materials for this article are available online.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:118:y:2023:i:544:p:2712-2720

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DOI: 10.1080/01621459.2022.2071720

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