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Bartlett's formula for a general class of nonlinear processes

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  • Christian Francq
  • Jean-Michel Zakoïan

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. Copyright 2009 Blackwell Publishing Ltd

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 30 (2009)
Issue (Month): 4 (07)
Pages: 449-465

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Handle: RePEc:bla:jtsera:v:30:y:2009:i:4:p:449-465

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  1. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  3. Christian Francq & Jean-Michel Zakoïan, 2008. "Barlett’s Formula for Non Linear Processes," Working Papers, Centre de Recherche en Economie et Statistique 2008-05, Centre de Recherche en Economie et Statistique.
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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, Wiley Blackwell, vol. 32(6), pages 699-723, November.
  2. Zakoïan, Jean-Michel & Regnard, Nazim, 2011. "A Conditionally Heteroskedastic Model with Time-varying Coefficients for Daily Gas Spot Prices," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/2603, Paris Dauphine University.
  3. Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(2), pages 345-361.
  4. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Su, Nan & Lund, Robert, 2012. "Multivariate versions of Bartlett’s formula," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 105(1), pages 18-31.
  6. Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2012. "Econometric modeling of exchange rate volatility and jumps," Working Papers, Federal Reserve Bank of St. Louis 2012-008, Federal Reserve Bank of St. Louis.

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