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Projection-based white noise and goodness-of-fit tests for functional time series

Author

Listed:
  • Mihyun Kim

    (West Virginia University)

  • Piotr Kokoszka

    (Colorado State University)

  • Gregory Rice

    (University of Waterloo)

Abstract

We develop two significance tests in the setting of functional time series. The null hypothesis of the first test is that the observed data are sampled from a general weak white noise sequence. The null hypothesis of the second test is that the observed data are sampled from a functional autoregressive model of order one (FAR(1)), which can be used as a goodness-of-fit test. Both tests are based on projections on functional principal components. Such projections are used in a great many functional data analysis (FDA) procedures, so our tests are practically relevant. We derive test statistics for each test that are quadratic forms of lagged autocovariance estimates constructed from principal component projections, and establish the requisite asymptotic theory. A simulation study shows that the tests have complimentary advantages against relevant benchmarks.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:27:y:2024:i:3:d:10.1007_s11203-024-09315-4
    DOI: 10.1007/s11203-024-09315-4
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    References listed on IDEAS

    as
    1. Zhang, Xianyang, 2016. "White noise testing and model diagnostic checking for functional time series," Journal of Econometrics, Elsevier, vol. 194(1), pages 76-95.
    2. Alexander Aue & Lajos Horváth & Daniel F. Pellatt, 2017. "Functional Generalized Autoregressive Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 3-21, January.
    3. 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.
    4. Cerovecki, Clément & Francq, Christian & Hörmann, Siegfried & Zakoïan, Jean-Michel, 2019. "Functional GARCH models: The quasi-likelihood approach and its applications," Journal of Econometrics, Elsevier, vol. 209(2), pages 353-375.
    5. Pramita Bagchi & Vaidotas Characiejus & Holger Dette, 2018. "A Simple Test for White Noise in Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(1), pages 54-74, January.
    6. Piotr Kokoszka & Matthew Reimherr, 2013. "Determining the order of the functional autoregressive model," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 116-129, January.
    7. Characiejus, Vaidotas & Rice, Gregory, 2020. "A general white noise test based on kernel lag-window estimates of the spectral density operator," Econometrics and Statistics, Elsevier, vol. 13(C), pages 175-196.
    8. Jacob Bien & Florentina Bunea & Luo Xiao, 2016. "Convex Banding of the Covariance Matrix," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 834-845, April.
    9. Gabrys, Robertas & Kokoszka, Piotr, 2007. "Portmanteau Test of Independence for Functional Observations," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1338-1348, December.
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