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A mixed portmanteau test for ARMA-GARCH model by the quasi-maximum exponential likelihood estimation approach

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  • Zhu, Ke
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Abstract

This paper investigates the joint limiting distribution of the residual autocorrelation functions and the absolute residual autocorrelation functions of ARMA-GARCH model. This leads a mixed portmanteau test for diagnostic checking of the ARMA-GARCH model fitted by using the quasi-maximum exponential likelihood estimation approach in Zhu and Ling (2011). Simulation studies are carried out to examine our asymptotic theory, and assess the performance of this mixed test and other two portmanteau tests in Li and Li (2008). A real example is given.

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File URL: http://mpra.ub.uni-muenchen.de/40382/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40382.

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Date of creation: 31 Jul 2012
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Handle: RePEc:pra:mprapa:40382

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Keywords: ARMA-GARCH model; LAD estimator; mixed portmanteau test; model diagnostics; quasi-maximum exponential likelihood estimator;

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  1. Francq, Christian & Lepage, Guillaume & Zakoïan, Jean-Michel, 2011. "Two-stage non Gaussian QML estimation of GARCH models and testing the efficiency of the Gaussian QMLE," Journal of Econometrics, Elsevier, vol. 165(2), pages 246-257.
  2. H. Wong & W. Li, 2002. "Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(1), pages 45-59, March.
  3. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
  4. Shao, Xiaofeng, 2011. "Testing For White Noise Under Unknown Dependence And Its Applications To Diagnostic Checking For Time Series Models," Econometric Theory, Cambridge University Press, vol. 27(02), pages 312-343, April.
  5. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  6. Heung Wong & Shiqing Ling, 2005. "Mixed Portmanteau Tests for Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 569-579, 07.
  7. Carbon, Michel & Francq, Christian, 2010. "Portmanteau goodness-of-fit test for asymmetric power GARCH models," MPRA Paper 27686, University Library of Munich, Germany.
  8. Berkes, Istv n & Horv th, Lajos & Kokoszka, Piotr, 2003. "Asymptotics For Garch Squared Residual Correlations," Econometric Theory, Cambridge University Press, vol. 19(04), pages 515-540, August.
  9. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
  10. Guodong Li & Wai Keung Li, 2008. "Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity," Biometrika, Biometrika Trust, vol. 95(2), pages 399-414.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. Guodong Li & Wai Keung Li, 2005. "Diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach," Biometrika, Biometrika Trust, vol. 92(3), pages 691-701, September.
  13. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
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