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Detection of EXPAR nonlinearity in the Presence of a Nuisance Unidentified Under the Null Hypothesis

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  • Nabil Azouagh

    (Université Mohammed Premier)

  • Said El Melhaoui

    (Université Mohammed Premier)

Abstract

This work considers the problem of detecting the eventual existence of an exponential component in autoregressive models of order p ≥ 1. This problem comes down to test a linear dependence AR(p) against a nonlinear one of exponential autoregressive model EXPAR(p). Following Le Cam’s asymptotic theory, we have established the local asymptotic normality of EXPAR(p) models in the vicinity of AR(p) ones. Then, we have used pseudo-Gaussian methods to extract a pseudo-Gaussian test which is locally asymptotically optimal under Gaussian densities and valid under a large class of non-Gaussian ones. The main problem arising in this context is the fact that the test statistic’s involves nuisance parameter unidentified under the null hypothesis. Contrary to the simple case of order 1 the test statistic’s depends on this nuisance through a complex function. So as to solve this problem, we suggest a method which consists to take the maximum of the test statistic’s over a specific compact set of the nuisance parameter, then, we use the AR-sieve bootstrap procedure to approximate its asymptotic distribution.

Suggested Citation

  • Nabil Azouagh & Said El Melhaoui, 2021. "Detection of EXPAR nonlinearity in the Presence of a Nuisance Unidentified Under the Null Hypothesis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 397-429, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-019-00209-7
    DOI: 10.1007/s13571-019-00209-7
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    References listed on IDEAS

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    1. Marc Hallin & Madan Lal Puri, 1994. "Aligned rank tests for linear models with autocorrelated errors," ULB Institutional Repository 2013/2045, ULB -- Universite Libre de Bruxelles.
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