• Corpus ID: 220364524

The maximum of the periodogram of Hilbert space valued time series.

@article{Cerovecki2020TheMO,
  title={The maximum of the periodogram of Hilbert space valued time series.},
  author={Cl{\'e}ment Cerovecki and Vaidotas Characiejus and Siegfried Hormann},
  journal={arXiv: Statistics Theory},
  year={2020}
}
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… 
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