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Bootstrapping covariance operators of functional time series

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  • Olimjon Sh. Sharipov
  • Martin Wendler

Abstract

For testing hypothesis on the covariance operator of functional time series, we suggest to use the full functional information and to avoid dimension reduction techniques. The limit distribution follows from the central limit theorem of the weak convergence of the partial sum process in general Hilbert space applied to the product space. In order to obtain critical values for tests, we generalise bootstrap results from the independent to the dependent case. This results can be applied to covariance operators, autocovariance operators and cross covariance operators. We discuss one sample and changepoint tests and give some simulation results.

Suggested Citation

  • Olimjon Sh. Sharipov & Martin Wendler, 2020. "Bootstrapping covariance operators of functional time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(3), pages 648-666, July.
    • Handle: RePEc:taf:gnstxx:v:32:y:2020:i:3:p:648-666
    DOI: 10.1080/10485252.2020.1771334
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    Cited by:

    1. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2022. "Change point analysis of covariance functions: A weighted cumulative sum approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Holger Dette & Kevin Kokot, 2022. "Detecting relevant differences in the covariance operators of functional time series: a sup-norm approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 195-231, April.

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