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

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  • Francq, Christian
  • Zakoian, Jean-Michel

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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File URL: https://mpra.ub.uni-muenchen.de/13224/1/MPRA_paper_13224.pdf
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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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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 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; Diffusion Processes

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. Christian Francq & Jean-Michel Zakoïan, 2008. "Barlett’s Formula for Non Linear Processes," Working Papers 2008-05, Centre de Recherche en Economie et Statistique.
  3. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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Cited by:

  1. Christian Francq & Roch Roy & Abdessamad Saidi, 2011. "Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(6), pages 699-723, November.
  2. Tommaso Proietti & Alessandra Luati, 2013. "The Generalised Autocovariance Function," CEIS Research Paper 276, Tor Vergata University, CEIS, revised 30 Apr 2013.
  3. Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2012. "Econometric modeling of exchange rate volatility and jumps," Working Papers 2012-008, Federal Reserve Bank of St. Louis.
  4. Su, Nan & Lund, Robert, 2012. "Multivariate versions of Bartlett’s formula," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 18-31.
  5. Boubacar Mainassara, Yacouba & Carbon, Michel & Francq, Christian, 2010. "Computing and estimating information matrices of weak arma models," MPRA Paper 27685, University Library of Munich, Germany.
  6. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. repec:dau:papers:123456789/2603 is not listed on IDEAS

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