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Whittle estimation of EGARCH and other exponential volatility models

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  • Zaffaroni, Paolo

Abstract

The strong consistency and asymptotic normality of the Whittle estimate of the parameters in a class of exponential volatility processes are established. Our main focus here are the EGARCH model of [Nelson, D. 1991. Conditional heteroscedasticity in asset pricing: A new approach. Econometrica 59, 347-370] and other one-shock models such as the GJR model of [Glosten, L., Jaganathan, R., Runkle, D., 1993. On the relation between the expected value and the volatility of the nominal excess returns on stocks. Journal of Finance, 48, 1779-1801], but two-shock models, such as the SV model of [Taylor, S. 1986. Modelling Financial Time Series. Wiley, Chichester, UK], are also comprised by our assumptions. The variable of interest might not have finite fractional moment of any order and so, in particular, finite variance is not imposed. We allow for a wide range of degrees of persistence of shocks to conditional variance, allowing for both short and long memory.

Suggested Citation

  • Zaffaroni, Paolo, 2009. "Whittle estimation of EGARCH and other exponential volatility models," Journal of Econometrics, Elsevier, vol. 151(2), pages 190-200, August.
    • Handle: RePEc:eee:econom:v:151:y:2009:i:2:p:190-200
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    3. Shelton Peiris & Manabu Asai & Michael McAleer, 2017. "Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models," JRFM, MDPI, vol. 10(4), pages 1-16, December.
    4. Hafner C. & Linton, O., 2013. "An Almost Closed Form Estimator for the EGARCH," LIDAM Discussion Papers ISBA 2013010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. 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.
    6. Yuanhua Feng & Thomas Gries & Sebastian Letmathe, 2023. "FIEGARCH, modulus asymmetric FILog-GARCH and trend-stationary dual long memory time series," Working Papers CIE 156, Paderborn University, CIE Center for International Economics.
    7. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2017. "Realized stochastic volatility with general asymmetry and long memory," Journal of Econometrics, Elsevier, vol. 199(2), pages 202-212.
    8. Filip Žikeš & Jozef Baruník & Nikhil Shenai, 2017. "Modeling and forecasting persistent financial durations," Econometric Reviews, Taylor & Francis Journals, vol. 36(10), pages 1081-1110, November.
    9. Hafner, Christian M. & Linton, Oliver, 2017. "An Almost Closed Form Estimator For The Egarch Model," Econometric Theory, Cambridge University Press, vol. 33(4), pages 1013-1038, August.
    10. Wintenberger, Olivier & Cai, Sixiang, 2011. "Parametric inference and forecasting in continuously invertible volatility models," MPRA Paper 31767, University Library of Munich, Germany.
    11. Fu, Yang & Zheng, Zeyu, 2020. "Volatility modeling and the asymmetric effect for China’s carbon trading pilot market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    12. Ruiz Esther & Pérez Ana, 2012. "Maximally Autocorrelated Power Transformations: A Closer Look at the Properties of Stochastic Volatility Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-33, September.
    13. Kraicová Lucie & Baruník Jozef, 2017. "Estimation of long memory in volatility using wavelets," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-22, June.
    14. Asai, Manabu & McAleer, Michael & Peiris, Shelton, 2020. "Realized stochastic volatility models with generalized Gegenbauer long memory," Econometrics and Statistics, Elsevier, vol. 16(C), pages 42-54.
    15. Royer, Julien, 2023. "Conditional asymmetry in Power ARCH(∞) models," Journal of Econometrics, Elsevier, vol. 234(1), pages 178-204.
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    17. Balli, Faruk & de Bruin, Anne & Chowdhury, Md Iftekhar Hasan, 2019. "Spillovers and the determinants in Islamic equity markets," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    18. Antonis Demos & Dimitra Kyriakopoulou, 2011. "Bias Correction of ML and QML Estimators in the EGARCH(1,1) Model," DEOS Working Papers 1108, Athens University of Economics and Business.
    19. Chih-Wen Hsiao & Ya-Chuan Chan & Mei-Yu Lee & Hsi-Peng Lu, 2021. "Heteroscedasticity and Precise Estimation Model Approach for Complex Financial Time-Series Data: An Example of Taiwan Stock Index Futures before and during COVID-19," Mathematics, MDPI, vol. 9(21), pages 1-18, October.
    20. Sucarrat, Genaro, 2010. "The power log-GARCH model," UC3M Working papers. Economics we1013, Universidad Carlos III de Madrid. Departamento de Economía.
    21. Royer, Julien, 2021. "Conditional asymmetry in Power ARCH($\infty$) models," MPRA Paper 109118, University Library of Munich, Germany.

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