The maximum of the periodogram of Hilbert space valued time series

Autor:	Cerovecki, Clément, Characiejus, Vaidotas, Hörmann, Siegfried
Rok vydání:	2020
Předmět:	Mathematics - Statistics Theory 62G32 62M10 (Primary) 62M15 62R10 62G10 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We are interested to detect periodic signals in Hilbert space valued time series when the length of the period is unknown. A natural test statistic is the maximum Hilbert-Schmidt norm of the periodogram operator over all fundamental frequencies. In this paper we analyze the asymptotic distribution of this test statistic. We consider the case where the noise variables are independent and then generalize our results to functional linear processes. Details for implementing the test are provided for the class of functional autoregressive processes. We illustrate the usefulness of our approach by examining air quality data from Graz, Austria. The accuracy of the asymptotic theory in finite samples is evaluated in a simulation experiment. Comment: 42 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.02188 Zobrazit plný text záznamu View this record from Arxiv