Testing nonstationary and absolutely regular nonlinear time series models

  • Joseph Ngatchou-WandjiEmail author
  • Madan L. Puri
  • Michel Harel
  • Echarif Elharfaoui


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.


Time series Nonstationarity Tests Local power of tests Weak convergence 

Mathematics Subject Classification

62M10 60F17 62J02 



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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Joseph Ngatchou-Wandji
    • 1
    Email author
  • Madan L. Puri
    • 2
  • Michel Harel
    • 3
    • 4
  • Echarif Elharfaoui
    • 5
  1. 1.EHESP Sorbonne Paris CitéInstitut Élie Cartan de LorraineVandoeuvre-lès-Nancy CedexFrance
  2. 2.Indiana UniversityBloomingtonUSA
  3. 3.ÉSPÉ de l’Académie de LimogesLimoges CedexFrance
  4. 4.Institut de Mathématiques de Toulouse UMR 5219 UPSToulouseFrance
  5. 5.Faculté des SciencesUniversité Chouaîb DoukkaliEl JadidaMorocco

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