Rank-based tests for autoregressive against bilinear serial dependence

Abstract

Opumal (signed and unsigned) rank-based procedures are derived for the problem of testing autoregiessive AR(l) dependence, with unspecified autoregressive parameter and innovation density, against firstorder 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.

Keywords:

• time series
• bilinear model
• bispectrum
• test of linearity
• rank test
• aligned ranks

AMS 1980 Subject classification:

• 62M10
• 62G10
• 62F05

^† Research supported by the Human Capital contract ERB CT CHRX 940 963 and the Fonds d'Encouragement á la Recherche de l'Université Libre de Bruxelles.

^† Research supported by the Human Capital contract ERB CT CHRX 940 963 and the Fonds d'Encouragement á la Recherche de l'Université Libre de Bruxelles.

Notes

^† Research supported by the Human Capital contract ERB CT CHRX 940 963 and the Fonds d'Encouragement á la Recherche de l'Université Libre de Bruxelles.