Locally asymptotically optimal tests for AR(p) against diagonal bilinear dependence

The problem of testing linear AR(p(1)) against diagonal bilinear BL(p(1),0; p(2), p(2)) dependence is considered. Emphasis is put on local asymptotic optimality and the nonspecification of innovation densities. The tests we are deriving are asymptotically valid under a large class of densities, and locally asymptotically most stringent at some selected density f. They rely on generalized versions of residual autocorrelations (the spectrum), and generalized versions of the so-called cubic autocorrelations (the bispectrum). Local powers are explicitly provided. The local power of the Gaussian Lagrange multipliers method follows as a particular case. (C) 1998 Elsevier Science B.V. All rights reserved.