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Testing nonstationary and absolutely regular nonlinear time series models

Author

Listed:
  • Joseph Ngatchou-Wandji

    (Institut Élie Cartan de Lorraine)

  • Madan L. Puri

    (Indiana University)

  • Michel Harel

    (ÉSPÉ de l’Académie de Limoges
    Institut de Mathématiques de Toulouse UMR 5219 UPS)

  • Echarif Elharfaoui

    (Université Chouaîb Doukkali)

Abstract

We study some general methods for testing the goodness-of-fit of a general nonstationary and absolutely regular nonlinear time series model. These testing methods are based on some marked empirical processes that we show to converge in distribution to a zero-mean Gaussian process with respect to the Skorohod topology. We investigate the behavior of this process under fixed alternatives and under a sequence of local alternatives. Our results are applied to testing a general class of nonlinear semiparametric time series models. A simulation experiment shows that the Cramér–von Mises test studied behaves well on the examples considered.

Suggested Citation

  • Joseph Ngatchou-Wandji & Madan L. Puri & Michel Harel & Echarif Elharfaoui, 2019. "Testing nonstationary and absolutely regular nonlinear time series models," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 557-593, October.
    • Handle: RePEc:spr:sistpr:v:22:y:2019:i:3:d:10.1007_s11203-018-9194-8
    DOI: 10.1007/s11203-018-9194-8
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    References listed on IDEAS

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