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

Nabil Azouagh () and Said El Melhaoui
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Nabil Azouagh: Université Mohammed Premier
Said El Melhaoui: Université Mohammed Premier

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 2, No 4, 397-429

Abstract: 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: Nonlinearity tests; Exponential autoregressive models; LAN property; Pseudo-Gaussian methods; Nuisance parameter; AR-sieve bootstrap; Primary 62G10; Secondary 62F05; 62F40 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13571-019-00209-7

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