Optimal detection of periodicities in vector autoregressive models

Marc Hallin and Soumia Lotfi

ULB Institutional Repository from ULB -- Universite Libre de Bruxelles

Abstract: Locally asymptotically optimal tests for testing stationary against periodic AR(p) dependence have been constructed by Bentarzi and Hallin (1996) in the univariate setting. These tests are generalized here to the multivariate context. A local asymptotic normality property is derived for m-variate d-periodic VAR(p) models in the vicinity of the stationary ones. The central sequence and the locally optimal tests are expressed in terms of a generalized concept of residual cross-covariance matrices. © 2005 Springer Science+Business Media, Inc.

Date: 2004
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