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On the limit theory of the Gaussian SQMLE in the EGARCH(1,1) model

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  • Stelios Arvanitis
  • Sofia Anyfantaki

Abstract

We derive the limit theory of the Gaussian stable quasi maximum likelihood estimator for the stationary EGARCH(1,1) model when the squared innovation process has marginals with regularly varying tails. We derive regularly varying rates and limiting stable distributions. We perform Monte Carlo experiments to assess the extent of the parameter space corresponding to the invertibility condition, and the quality of the asymptotic approximation.

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  • Stelios Arvanitis & Sofia Anyfantaki, 2020. "On the limit theory of the Gaussian SQMLE in the EGARCH(1,1) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 341-350, March.
    • Handle: RePEc:bla:jtsera:v:41:y:2020:i:2:p:341-350
    DOI: 10.1111/jtsa.12494
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    References listed on IDEAS

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    1. 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.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    3. Demos Antonis & Kyriakopoulou Dimitra, 2019. "Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-20, January.
    4. Olivier Wintenberger, 2013. "Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 846-867, December.
    5. 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.
    6. Arvanitis, Stelios & Louka, Alexandros, 2017. "Stable limits for the Gaussian QMLE in the non-stationary GARCH(1,1) model," Economics Letters, Elsevier, vol. 161(C), pages 135-137.
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