Bartlett's Formula for a General Class of Nonlinear Processes

17 Pages Posted: 20 Jun 2009

See all articles by Christian Francq

Christian Francq

University of Lille III

Jean-Michel Zakoïan

Université de Lille III

Date Written: 0000

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. It is illustrated on ARMA–GARCH models and compared to the standard formula. An empirical application on financial time series is proposed.

Suggested Citation

Francq, Christian and Zakoian, Jean-Michel, Bartlett's Formula for a General Class of Nonlinear Processes (0000). Journal of Time Series Analysis, Vol. 30, Issue 4, pp. 449-465, July 2009. Available at SSRN: https://ssrn.com/abstract=1423152 or http://dx.doi.org/10.1111/j.1467-9892.2009.00623.x

Christian Francq

University of Lille III ( email )

Domaine du Pont de bois
Villeneuve D'Ascq Cedex, 59653
France

Jean-Michel Zakoian

Université de Lille III ( email )

Domaine du Pont de bois
Villeneuve D'Ascq Cedex, 59653
France

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