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Sankhya B

pp 1–33 | Cite as

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

  • Nabil AzouaghEmail author
  • Said El Melhaoui
Article
  • 5 Downloads

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.

Keywords and phrases.

Nonlinearity tests Exponential autoregressive models LAN property Pseudo-Gaussian methods Nuisance parameter AR-sieve bootstrap 

AMS (2000) subject classification.

Primary 62G10 Secondary 62F05 62F40 

Notes

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Copyright information

© Indian Statistical Institute 2019

Authors and Affiliations

  1. 1.Faculté des Sciences, Département de MathématiquesUniversité Mohammed PremierOujdaMorocco
  2. 2.Faculté de Droit, Département d’ÉconomieUniversité Mohammed PremierOujdaMorocco

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