Testing nonstationary and absolutely regular nonlinear time series models

Joseph Ngatchou-Wandji (), Madan L. Puri, Michel Harel and Echarif Elharfaoui
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Joseph Ngatchou-Wandji: Institut Élie Cartan de Lorraine
Madan L. Puri: Indiana University
Michel Harel: ÉSPÉ de l’Académie de Limoges
Echarif Elharfaoui: Université Chouaîb Doukkali

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 3, No 8, 557-593

Abstract: 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.

Keywords: Time series; Nonstationarity; Tests; Local power of tests; Weak convergence; 62M10; 60F17; 62J02 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11203-018-9194-8

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