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Estimating GARCH models: when to use what?

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  • Huang, Da
  • Wang, Hansheng
  • Yao, Qiwei

Abstract

The class of generalized autoregressive conditional heteroscedastic (GARCH) models has proved particularly valuable in modelling time series with time varying volatility. These include financial data, which can be particularly heavy tailed. It is well understood now that the tail heaviness of the innovation distribution plays an important role in determining the relative performance of the two competing estimation methods, namely the maximum quasi-likelihood estimator based on a Gaussian likelihood (GMLE) and the log-transform-based least absolutely deviations estimator (LADE) (see Peng and Yao 2003Biometrika,90, 967–75). A practically relevant question is when to use what. We provide in this paper a solution to this question. By interpreting the LADE as a version of the maximum quasilikelihood estimator under the likelihood derived from assuming hypothetically that the log-squared innovations obey a Laplace distribution, we outline a selection procedure based on some goodness-of-fit type statistics. The methods are illustrated with both simulated and real data sets. Although we deal with the estimation for GARCH models only, the basic idea may be applied to address the estimation procedure selection problem in a general regression setting.

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  • Huang, Da & Wang, Hansheng & Yao, Qiwei, 2008. "Estimating GARCH models: when to use what?," LSE Research Online Documents on Economics 5398, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:5398
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    References listed on IDEAS

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    1. 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.
    2. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
    3. Peng, Liang & Yao, Qiwei, 2003. "Least absolute deviations estimation for ARCH and GARCH models," LSE Research Online Documents on Economics 5828, London School of Economics and Political Science, LSE Library.
    4. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    5. Giraitis, Liudas & Robinson, Peter M., 2001. "Whittle Estimation Of Arch Models," Econometric Theory, Cambridge University Press, vol. 17(3), pages 608-631, June.
    6. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    7. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    8. Giraitis, Liudas & Robinson, Peter M., 2001. "Whittle estimation of ARCH models," LSE Research Online Documents on Economics 316, London School of Economics and Political Science, LSE Library.
    9. 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.
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    Citations

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    Cited by:

    1. Koo, Bonsoo & Linton, Oliver, 2015. "Let’S Get Lade: Robust Estimation Of Semiparametric Multiplicative Volatility Models," Econometric Theory, Cambridge University Press, vol. 31(4), pages 671-702, August.
    2. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    3. De Santis, Paola & Drago, Carlo, 2014. "Asimmetria del rischio sistematico dei titoli immobiliari americani: nuove evidenze econometriche [Systematic Risk Asymmetry of the American Real Estate Securities: Some New Econometric Evidence]," MPRA Paper 59381, University Library of Munich, Germany.
    4. Ken Miyajima, 2020. "Exchange rate volatility and pass‐through to inflation in South Africa," African Development Review, African Development Bank, vol. 32(3), pages 404-418, September.
    5. Klar, B. & Lindner, F. & Meintanis, S.G., 2012. "Specification tests for the error distribution in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3587-3598.
    6. Preminger, Arie & Storti, Giuseppe, 2014. "Least squares estimation for GARCH (1,1) model with heavy tailed errors," MPRA Paper 59082, University Library of Munich, Germany.
    7. Carnero M. Angeles & Pérez Ana, 2021. "Outliers and misleading leverage effect in asymmetric GARCH-type models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(1), pages 1-19, February.
    8. Spierdijk, Laura, 2016. "Confidence intervals for ARMA–GARCH Value-at-Risk: The case of heavy tails and skewness," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 545-559.
    9. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    10. Meintanis, Simos G. & Tsionas, Efthimios, 2010. "Testing for the generalized normal-Laplace distribution with applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3174-3180, December.

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    More about this item

    Keywords

    estimation procedure selection; GARCH; Gaussian likelihood; heavy tail; laplace distribution; least absolute deviations estimator; maximum quasilikelihood estimator;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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