Testing serial independence with functional data

• Zdeněk Hlávka ^[1] ; Marie Hušková ^[1] ; Simos G. Meintanis ^[2]
  1. [1] Charles University in Prague

     Charles University in Prague

     Chequia

     
  2. [2] National and Kapodistrian University of Athens

     National and Kapodistrian University of Athens

     Dimos Athens, Grecia

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 30, Nº. 3, 2021, págs. 603-629
• Idioma: inglés
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• Resumen

  • 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.