Barlett’s Formula for Non Linear Processes

Christian Francq and Jean-Michel Zakoian

No 2008-05, Working Papers from Center for Research in Economics and Statistics

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.

Pages: 18
Date: 2008
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Citations: View citations in EconPapers (2)

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