A mixed portmanteau test for ARMA-GARCH model by the quasi-maximum exponential likelihood estimation approach
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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- Ling, Shiqing & McAleer, Michael, 2003.
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- 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.
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- 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.
- 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.
- Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
- 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.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- 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.
- 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.
- Carbon, Michel & Francq, Christian, 2010. "Portmanteau goodness-of-fit test for asymmetric power GARCH models," MPRA Paper 27686, University Library of Munich, Germany.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
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