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Normal Mixture Quasi‐maximum Likelihood Estimator for GARCH Models

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  • TAEWOOK LEE
  • SANGYEOL LEE

Abstract

. The generalized autoregressive conditional heteroscedastic (GARCH) model has been popular in the analysis of financial time series data with high volatility. Conventionally, the parameter estimation in GARCH models has been performed based on the Gaussian quasi‐maximum likelihood. However, when the innovation terms have either heavy‐tailed or skewed distributions, the quasi‐maximum likelihood estimator (QMLE) does not function well. In order to remedy this defect, we propose the normal mixture QMLE (NM‐QMLE), which is obtained from the normal mixture quasi‐likelihood, and demonstrate that the NM‐QMLE is consistent and asymptotically normal. Finally, we present simulation results and a real data analysis in order to illustrate our findings.

Suggested Citation

  • Taewook Lee & Sangyeol Lee, 2009. "Normal Mixture Quasi‐maximum Likelihood Estimator for GARCH Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 157-170, March.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:1:p:157-170
    DOI: 10.1111/j.1467-9469.2008.00624.x
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    Cited by:

    1. Lee, Sangyeol & Tim Ng, Chi, 2010. "Trimmed portmanteau test for linear processes with infinite variance," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 984-998, April.
    2. Caporin, Massimiliano & Rossi, Eduardo & Santucci de Magistris, Paolo, 2017. "Chasing volatility," Journal of Econometrics, Elsevier, vol. 198(1), pages 122-145.
    3. Fiorentini, Gabriele & Sentana, Enrique, 2023. "Discrete mixtures of normals pseudo maximum likelihood estimators of structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 235(2), pages 643-665.
    4. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.
    5. Lee, Sangyeol & Ng, Chi Tim, 2011. "Normality test for multivariate conditional heteroskedastic dynamic regression models," Economics Letters, Elsevier, vol. 111(1), pages 75-77, April.
    6. Hwang, S.Y. & Baek, J.S. & Park, J.A. & Choi, M.S., 2010. "Explosive volatilities for threshold-GARCH processes generated by asymmetric innovations," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 26-33, January.
    7. Ha, Jeongcheol & Lee, Taewook, 2011. "NM-QELE for ARMA-GARCH models with non-Gaussian innovations," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 694-703, June.

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