Bartlett's formula for a general class of non linear processes
AbstractA 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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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 13224.
Date of creation: 05 Feb 2009
Date of revision:
Bartlett's formula; nonlinear time series model; sample autocorrelation; GARCH model; weak white noise;
Other versions of this item:
- 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, 07.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-02-14 (All new papers)
- NEP-ECM-2009-02-14 (Econometrics)
- NEP-ETS-2009-02-14 (Econometric Time Series)
- NEP-ORE-2009-02-14 (Operations Research)
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