Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models
This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA–GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given for some cases. A simulation study is carried out to assess the performance of these estimators, and a real example on the world crude oil price is given.
|Date of creation:||17 Nov 2013|
|Publication status:||Published in Annals of Statistics 4.39(2011): pp. 2131-2163|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
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- Ling, Shiqing & McAleer, Michael, 2003.
"Asymptotic Theory For A Vector Arma-Garch Model,"
Cambridge University Press, vol. 19(02), pages 280-310, April.
- 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.
- 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.
- Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
- 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.
- Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
- Zhu, Ke & Ling, Shiqing, 2012. "THE GLOBAL WEIGHTED LAD ESTIMATORS FOR FINITE/INFINITE VARIANCE ARMA(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1065-1086, October.
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
- 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.
- Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
- Rongning Wu & Richard A. Davis, 2010. "Least absolute deviation estimation for general autoregressive moving average time-series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 98-112, March.
- Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
- 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.
- Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
- Shiqing Ling, 2005. "Self-weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393.
- Ngai Hang Chan & Liang Peng, 2005. "Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors," Biometrika, Biometrika Trust, vol. 92(2), pages 477-484, June.
- Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
- Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
- 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.
- Pan, Jiazhu & Wang, Hui & Yao, Qiwei, 2007. "Weighted Least Absolute Deviations Estimation For Arma Models With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 23(05), pages 852-879, October.
- Theis Lange & Anders Rahbek & Søren Tolver Jensen, 2011. "Estimation and Asymptotic Inference in the AR-ARCH Model," Econometric Reviews, Taylor & Francis Journals, vol. 30(2), pages 129-153. Full references (including those not matched with items on IDEAS)
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