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

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Author Info
Francq, Christian
Zakoian, Jean-Michel

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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 13224.

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Date of creation: 05 Feb 2009
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Handle: RePEc:pra:mprapa:13224

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Related research
Keywords: Bartlett's formula; nonlinear time series model; sample autocorrelation; GARCH model; weak white noise;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
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