The maximum of the periodogram of a sequence of functional data

Clément Cerovecki, Vaidotas Characiejus*, Siegfried Hörmann

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


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.

Original languageEnglish
JournalJournal of the American Statistical Association
Publication statusE-pub ahead of print - 2. Jun 2022

Bibliographical note

Publisher Copyright:
© 2022 American Statistical Association.


  • Deseasonalizing data
  • Functional data
  • Periodicities
  • Periodogram
  • Time series


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