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Rank-based tests for autoregressive against bilinear serial dependence

par Hallin, Marc ;Benghabrit, Youssef
Référence Journal of Nonparametric Statistics, 6, 2-3, page (253-272)
Publication Publié, 1996

Article révisé par les pairs

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Résumé :

Optimal (signed and unsigned) rank-based procedures are derived for the problem of testing autoregressive AR(1) dependence, with unspecified autoregressive parameter and innovation density, against first-order diagonal bilinear dependence. The proposed test statistics rely on rank-based versions of the residual spectrum and bispectrum. The resulting tests are asymptotically invariant, hence asymptotically distribution-free, and locally asymptotically most powerful. Their local asymptotic powers and asymptotic relative efficiencies with respect to the Gaussian Lagrange multiplier procedure of Saikkonen and Luukkonen (1988) are provided explicitly.