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Optimal Detection of Periodicities in Vector Autoregressive Models

In: Statistical Modeling and Analysis for Complex Data Problems

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  • Marc Hallin
  • Soumia Lotfi

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.

Suggested Citation

  • Marc Hallin & Soumia Lotfi, 2005. "Optimal Detection of Periodicities in Vector Autoregressive Models," Springer Books, in: Pierre Duchesne & Bruno RÉMillard (ed.), Statistical Modeling and Analysis for Complex Data Problems, chapter 0, pages 281-307, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-24555-3_14
    DOI: 10.1007/0-387-24555-3_14
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