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Testing serial independence with functional data

Author

Listed:
  • Zdeněk Hlávka

    (Charles University, Faculty of Mathematics and Physics)

  • Marie Hušková

    (Charles University, Faculty of Mathematics and Physics)

  • Simos G. Meintanis

    (National and Kapodistrian University of Athens
    North-West University)

Abstract

We consider tests of serial independence for a sequence of functional observations. The new methods are formulated as L2-type criteria based on empirical characteristic functions and are convenient from the computational point of view. We derive asymptotic normality of the proposed test statistics for both discretely and continuously observed functions. In a Monte Carlo study, we show that the new test is sensitive with respect to functional GARCH alternatives, investigate the choice of necessary tuning parameters, and demonstrate that critical values obtained by resampling lead to a test with good performance in any setup, whereas the asymptotic critical values may be recommended only for a sufficiently fine discretization grid. Finite-sample comparison with a distance (auto)covariance test criterion is also included, and the article concludes with application on a real data set.

Suggested Citation

  • Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2021. "Testing serial independence with functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 603-629, September.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:3:d:10.1007_s11749-020-00732-0
    DOI: 10.1007/s11749-020-00732-0
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    References listed on IDEAS

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    Cited by:

    1. Meintanis, Simos G. & Hušková, Marie & Hlávka, Zdeněk, 2022. "Fourier-type tests of mutual independence between functional time series," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Mihyun Kim & Piotr Kokoszka & Gregory Rice, 2024. "Projection-based white noise and goodness-of-fit tests for functional time series," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 693-724, October.
    3. Matsui, Muneya & Mikosch, Thomas & Roozegar, Rasool & Tafakori, Laleh, 2022. "Distance covariance for random fields," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 280-322.
    4. Petr Čoupek & Viktor Dolník & Zdeněk Hlávka & Daniel Hlubinka, 2024. "Fourier approach to goodness-of-fit tests for Gaussian random processes," Statistical Papers, Springer, vol. 65(5), pages 2937-2972, July.
    5. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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