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AdaVol: An Adaptive Recursive Volatility Prediction Method

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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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    2. 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.
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    Cited by:

    1. Simon Hirsch & Jonathan Berrisch & Florian Ziel, 2024. "Online Distributional Regression," Papers 2407.08750, arXiv.org, revised Aug 2024.
    2. 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, revised Jun 2024.

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    Keywords

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