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AdaVol: An Adaptive Recursive Volatility Prediction Method

Author

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  • Nicklas Werge

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

  • Olivier Wintenberger

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

Abstract

Quasi-Maximum Likelihood (QML) procedures are theoretically appealing and widely used for statistical inference. While there are extensive references on QML estimation in batch settings, the QML estimation in streaming settings has attracted little attention until recently. An investigation of the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model is conducted, and the classical batch optimization routines extended to the framework of streaming and large-scale problems. An adaptive recursive estimation routine for GARCH models named AdaVol is presented. The AdaVol procedure relies on stochastic approximations combined with the technique of Variance Targeting Estimation (VTE). This recursive method has computationally efficient properties, while VTE alleviates some convergence difficulties encountered by the usual QML estimation due to a lack of convexity. Empirical results demonstrate a favorable trade-off between AdaVol's stability and the ability to adapt to time-varying estimates for real-life data.

Suggested Citation

  • Nicklas Werge & Olivier Wintenberger, 2022. "AdaVol: An Adaptive Recursive Volatility Prediction Method," Post-Print hal-02733439, HAL.
    • Handle: RePEc:hal:journl:hal-02733439
    DOI: 10.1016/j.ecosta.2021.01.004
    Note: View the original document on HAL open archive server: https://hal.science/hal-02733439v3
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    References listed on IDEAS

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    1. Christian Francq & Lajos Horváth, 2011. "Merits and Drawbacks of Variance Targeting in GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 9(4), pages 619-656.
    2. Sucarrat, Genaro, 2020. "garchx: Flexible and Robust GARCH-X Modelling," MPRA Paper 100301, University Library of Munich, Germany.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    5. Ip, W.C. & Wong, Heung & Pan, J.Z. & Li, D.F., 2006. "The asymptotic convexity of the negative likelihood function of GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 311-331, January.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    7. 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.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    9. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    10. J. Pfanzagl, 1969. "On the measurability and consistency of minimum contrast estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 14(1), pages 249-272, December.
    11. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
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    Cited by:

    1. Joseph de Vilmarest & Nicklas Werge, 2023. "An adaptive volatility method for probabilistic forecasting and its application to the M6 financial forecasting competition," Papers 2303.01855, arXiv.org.

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    Keywords

    recursive algorithm; quasi-likelihood; volatility models; GARCH; prediction method; stock index;
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