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Barlett’s Formula for Non Linear Processes

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  • Christian Francq

    (Crest)

  • Jean-Michel Zakoïan

    (Crest)

Abstract

A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations ofnonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as thesum of two terms. The first term corresponds to the standard Bartlett’s formula for linear processes,involving only the autocorrelation function of the observed process. The second term, which is specificto nonlinear processes, involves the autocorrelation function of the observed process, the kurtosis of thelinear innovation process and the autocorrelation function of its square. This formula is obtained under asymmetry assumption on the linear innovation process. An application to GARCH models is proposed.

Suggested Citation

  • Christian Francq & Jean-Michel Zakoïan, 2008. "Barlett’s Formula for Non Linear Processes," Working Papers 2008-05, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2008-05
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    Cited by:

    1. Christian Francq & Jean-Michel Zakoïan, 2009. "Bartlett's formula for a general class of nonlinear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 449-465, July.
    2. Christian Francq & Roch Roy & Abdessamad Saidi, 2011. "Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(6), pages 699-723, November.

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