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An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation

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  • Francq, Christian
  • Sucarrat, Genaro

Abstract

Estimation of log-GARCH models via the ARMA representation is attractive because it enables a vast amount of already established results in the ARMA literature. We propose an exponential Chi-squared QMLE for log-GARCH models via the ARMA representation. The advantage of the estimator is that it corresponds to the theoretically and empirically important case where the conditional error of the log-GARCH model is normal. We prove the consistency and asymptotic normality of the estimator, and show that, asymptotically, it is as efficient as the standard QMLE in the log-GARCH(1,1) case. We also verify and study our results in finite samples by Monte Carlo simulations. An empirical application illustrates the versatility and usefulness of the estimator.

Suggested Citation

  • Francq, Christian & Sucarrat, Genaro, 2013. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," MPRA Paper 51783, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:51783
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    Cited by:

    1. Raffaele Mattera & Philipp Otto, 2023. "Network log-ARCH models for forecasting stock market volatility," Papers 2303.11064, arXiv.org.
    2. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    3. Francq, Christian & Sucarrat, Genaro, 2017. "An equation-by-equation estimator of a multivariate log-GARCH-X model of financial returns," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 16-32.
    4. Sucarrat, Genaro, 2018. "The Log-GARCH Model via ARMA Representations," MPRA Paper 100386, University Library of Munich, Germany.
    5. Yuanhua Feng & Jan Beran & Sebastian Letmathe & Sucharita Ghosh, 2020. "Fractionally integrated Log-GARCH with application to value at risk and expected shortfall," Working Papers CIE 137, Paderborn University, CIE Center for International Economics.
    6. Bonnier, Jean-Baptiste, 2022. "Forecasting crude oil volatility with exogenous predictors: As good as it GETS?," Energy Economics, Elsevier, vol. 111(C).

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    More about this item

    Keywords

    Log-GARCH; EGARCH; Quasi Maximum Likelihood; Exponential Chi- Squared; ARMA;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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