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Estimating GARCH models: when to use what?

Author

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  • Da Huang
  • Hansheng Wang
  • Qiwei Yao

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. Copyright Royal Economic Society 2008

Suggested Citation

  • Da Huang & Hansheng Wang & Qiwei Yao, 2008. "Estimating GARCH models: when to use what?," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 27-38, March.
  • Handle: RePEc:ect:emjrnl:v:11:y:2008:i:1:p:27-38
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    References listed on IDEAS

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    1. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    2. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 239-253.
    3. Pesaran, M.H., 2004. "‘General Diagnostic Tests for Cross Section Dependence in Panels’," Cambridge Working Papers in Economics 0435, Faculty of Economics, University of Cambridge.
    4. Frees, Edward W., 1995. "Assessing cross-sectional correlation in panel data," Journal of Econometrics, Elsevier, vol. 69(2), pages 393-414, October.
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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(04), pages 671-702, August.
    2. 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.
    3. 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.
    4. 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.
    5. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    6. 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.
    7. 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.
    8. 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.

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