Bartlett's formula for a general class of non linear processes

Christian Francq and Jean-Michel Zakoian

MPRA Paper from University Library of Munich, Germany

Abstract: A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations of nonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as the sum 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 specific to nonlinear processes, involves the autocorrelation function of the observed process, the kurtosis of the linear innovation process and the autocorrelation function of its square. This formula is obtained under a symmetry assumption on the linear innovation process. An application to GARCH models is proposed.

Keywords: Bartlett's formula; nonlinear time series model; sample autocorrelation; GARCH model; weak white noise (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 (search for similar items in EconPapers)
Date: 2009-02-05
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Citations: View citations in EconPapers (14)

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Journal Article: Bartlett's formula for a general class of nonlinear processes (2009)
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