Inference in Arch and Garch Models with Heavy--Tailed Errors
AbstractARCH and GARCH models directly address the dependency of conditional second moments, and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present. These include financial time series, which can be particularly heavy tailed. However, little is known about properties of ARCH or GARCH models in the heavy--tailed setting, and no methods are available for approximating the distributions of parameter estimators there. In this paper we show that, for heavy--tailed errors, the asymptotic distributions of quasi--maximum likelihood parameter estimators in ARCH and GARCH models are nonnormal, and are particularly difficult to estimate directly using standard parametric methods. Standard bootstrap methods also fail to produce consistent estimators. To overcome these problems we develop percentile--"t", subsample bootstrap approximations to estimator distributions. Studentizing is employed to approximate scale, and the subsample bootstrap is used to estimate shape. The good performance of this approach is demonstrated both theoretically and numerically. Copyright The Econometric Society 2003.
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Bibliographic InfoArticle provided by Econometric Society in its journal Econometrica.
Volume (Year): 71 (2003)
Issue (Month): 1 (January)
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- Russell Davidson & Emmanuel Flachaire, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Post-Print halshs-00175929, HAL.
- Enrique Sentana & Gabriele Fiorentini, 2007.
"On The Efficiency And Consistency Of Likelihood Estimation In Multivariate Conditionally Heteroskedastic Dynamic Regression Models,"
- Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper Series 38-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
- PREMINGER, Arie & STORTI, Giuseppe, 2006. "A GARCH (1,1) estimator with (almost) no moment conditions on the error term," CORE Discussion Papers 2006068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Davidson, Russell & Flachaire, Emmanuel, 2007.
"Asymptotic and bootstrap inference for inequality and poverty measures,"
Journal of Econometrics,
Elsevier, vol. 141(1), pages 141-166, November.
- Russell Davidson & Emmanuel Flachaire, 2006. "Asymptotic And Bootstrap Inference For Inequality And Poverty Measures," Departmental Working Papers 2005-06, McGill University, Department of Economics.
- Russell Davidson & Emmanuel Flachaire, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00175929, HAL.
- Russell Davidson & Emmanuel Flachaire, 2004. "Asymptotic and bootstrap inference for inequality and poverty measures," Cahiers de la Maison des Sciences Economiques v04100, Université Panthéon-Sorbonne (Paris 1).
- Elena Andreou & Eric Ghysels, 2004.
"The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests,"
CIRANO Working Papers
- Elena Andreou, 2004. "The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 290-318.
- Zhu, Ke & Li, Wai Keung, 2014.
"A new Pearson-type QMLE for conditionally heteroskedastic models,"
52732, University Library of Munich, Germany.
- Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
- Zakoïan, Jean-Michel & Regnard, Nazim, 2008. "GARCH (1,1) Models with Exogenously-Driven Volatility: Structure and Estimation," Economics Papers from University Paris Dauphine 123456789/2285, Paris Dauphine University.
- Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
- Chen, Min & Zhu, Ke, 2013. "Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations," MPRA Paper 50487, University Library of Munich, Germany.
- Frank A. Cowell & Emmanuel Flachaire, 2007. "Income distribution and inequality measurement: The problem of extreme values," Post-Print halshs-00176029, HAL.
- Emma Iglesias & Jean Marie Dufour, 2004. "Finite Sample and Optimal Inference in Possibly Nonstationary ARCH Models with Gaussian and Heavy-Tailed Errors," Econometric Society 2004 North American Summer Meetings 161, Econometric Society.
- Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
- Cowell, Frank A. & Flachaire, Emmanuel, 2007.
"Income distribution and inequality measurement: The problem of extreme values,"
Journal of Econometrics,
Elsevier, vol. 141(2), pages 1044-1072, December.
- Frank A. Cowell & Emmanuel Flachaire, 2004. "Income distribution and inequality measurement : the problem of extreme values," Cahiers de la Maison des Sciences Economiques v04101, Université Panthéon-Sorbonne (Paris 1).
- Frank A. Cowell & Emmanuel Flachaire, 2007. "Income distribution and inequality measurement: The problem of extreme values," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00176029, HAL.
- Christian Francq & Jean-Michel ZakoÃ¯an, 2006. "Inference in GARCH when some coefficients are equal to zero," Computing in Economics and Finance 2006 64, Society for Computational Economics.
- Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
- Jonathan B. Hill, 2005. "Gaussian Tests of "Extremal White Noise" for Dependent, Heterogeneous, Heavy Tailed Strochastic Processes with an Application," Working Papers 0513, Florida International University, Department of Economics.
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