Testing the goodness of fit of a hilbertian autoregressive model

  1. González-Manteiga, Wenceslao
  2. Ruiz-Medina, María Dolores
  3. López-Pérez, A. M.
  4. Álvarez-Liébana, Javier
Revista:
arXiv - MATH - Statistics Theory

Ano de publicación: 2023

Tipo: Artigo

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Resumo

The presented methodology for testing the goodness–of–fit of an Autoregressive Hilbertian model (ARH(1) model) provides an infinite–dimensional formulation of the approach proposed in Koul and Stute [38], based on empirical process marked by residuals. Applying a central and functional central limit result for Hilbert–valued martingale difference sequences, the asymptotic behavior of the formulated H–valued empirical process, also indexed by H, is obtained under the null hypothesis. Thelimiting process is H–valued generalized (i.e., indexed by H) Wiener process, leading to an asymptotically distribution free test. Consistency is also analyzed. The case of misspecified autocorrelation operator of the ARH(1) process is addressed as well. Beyond the Euclidean setting, this approach allows to implement goodness of fit testing in the context of manifold and spherical functional autoregressive processes.

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