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Title: Detection of periodic signals in functional time series Authors:  Vaidotas Characiejus - University of California, Davis (United States) [presenting]
Siegfried Hoermann - Graz University of Technology (Austria)
Clement Cerovecki - Katholieke Universiteit Leuven (Belgium)
Abstract: A test is developed to detect periodic signals in functional time series when the length of the period is unknown. The observations are assumed to belong to an infinite-dimensional separable Hilbert space and the test is based on the asymptotic distribution of the maximum over all Fourier frequencies of the Hilbert-Schmidt norm of the periodogram operator. We show that under certain assumptions the appropriately standardized maximum of the periodogram belongs to the domain of attraction of the Gumbel distribution. The main ingredient of the proof is a recent Gaussian approximation. The results generalize a previous result to multivariate and functional time series. They also complement other results, where the length of the period is assumed to be known. We illustrate the usefulness of our test by examining the air quality data from Graz, Austria, and showing that our test is able to reveal a periodic component which is not a priori expected. We also demonstrate the finite sample performance of our test using a small simulation study.