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Change-Point Detection in Functional First-Order Auto-Regressive Models

Author

Listed:
  • Algimantas Birbilas

    (Institute of Applied Mathematics, Vilnius University, Naugarduko g. 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Alfredas Račkauskas

    (Institute of Applied Mathematics, Vilnius University, Naugarduko g. 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

Abstract

A sample of continuous random functions with auto-regressive structures and possible change-point of the means are considered. We present test statistics for the change-point based on a functional of partial sums. To study their asymptotic behavior, we prove functional limit theorems for polygonal line processes in the space of continuous functions. For some situations, we use a block bootstrap procedure to construct the critical region and provide applications. We also study the finite sample behavior via simulations. Eventually, we apply the statistics to a telecommunications data sample.

Suggested Citation

  • Algimantas Birbilas & Alfredas Račkauskas, 2024. "Change-Point Detection in Functional First-Order Auto-Regressive Models," Mathematics, MDPI, vol. 12(12), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1889-:d:1417130
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    References listed on IDEAS

    as
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    3. Laura Aspirot & Karine Bertin & Gonzalo Perera, 2009. "Asymptotic normality of the Nadaraya–Watson estimator for nonstationary functional data and applications to telecommunications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 535-551.
    4. Aue, Alexander & Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2009. "Estimation of a change-point in the mean function of functional data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2254-2269, November.
    5. Horváth, Lajos & Reeder, Ron, 2012. "Detecting changes in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 310-334.
    6. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.
    7. J. Ramsay, 1982. "When the data are functions," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 379-396, December.
    Full references (including those not matched with items on IDEAS)

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