Bartlett's formula for a general class of nonlinear 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. It is illustrated on ARMA-GARCH models and compared to the standard formula. An empirical application on financial time series is proposed. Copyright 2009 Blackwell Publishing Ltd
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Journal of Time Series Analysis.
Volume (Year): 30 (2009)
Issue (Month): 4 (07)
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782
Other versions of this item:
- Francq, Christian & Zakoian, Jean-Michel, 2009. "Bartlett's formula for a general class of non linear processes," MPRA Paper 13224, University Library of Munich, Germany.
- 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
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