A0517
Title: The maximum of the periodogram of a sequence of functional data
Authors: Clement Cerovecki - Katholieke Universiteit Leuven (Belgium)
Siegfried Hoermann - Graz University of Technology (Austria)
Vaidotas Characiejus - University of Southern Denmark (Denmark) [presenting]
Abstract: The detection of periodic signals in functional time series is investigated when the length of the period is not assumed to be known. A natural test statistic for the detection of periodicities is the maximum overall fundamental frequencies of the Hilbert-Schmidt norm of the periodogram operator. Using recent advances in Gaussian approximation theory, we show that under certain assumptions the appropriately standardised test statistic belongs to the domain of attraction of the Gumbel distribution. The asymptotic results allow us to construct tests for hidden periodicities. We demonstrate the performance of our methodology in a simulation study and we also illustrate the usefulness of our approach by examining periodicities in the air quality data from Graz, Austria and showing that our approach is not only able to detect the presence of periodic signals but it is also able to reveal the structure of periodicities in the data.
