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Higher Moments and Prediction-Based Estimation for the COGARCH(1,1) Model

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  • Enrico Bibbona
  • Ilia Negri

Abstract

type="main" xml:id="sjos12142-abs-0001"> COGARCH models are continuous time versions of the well-known GARCH models of financial returns. The first aim of this paper is to show how the method of prediction-based estimating functions can be applied to draw statistical inference from observations of a COGARCH(1,1) model if the higher-order structure of the process is clarified. A second aim of the paper is to provide recursive expressions for the joint moments of any fixed order of the process. Asymptotic results are given, and a simulation study shows that the method of prediction-based estimating function outperforms the other available estimation methods.

Suggested Citation

  • Enrico Bibbona & Ilia Negri, 2015. "Higher Moments and Prediction-Based Estimation for the COGARCH(1,1) Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 891-910, December.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:4:p:891-910
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    File URL: http://hdl.handle.net/10.1111/sjos.12142
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    References listed on IDEAS

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    1. S. Haug & C. Klüppelberg & A. Lindner & M. Zapp, 2007. "Method of moment estimation in the COGARCH(1,1) model," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 320-341, July.
    2. Ross A. Maller & Gernot Muller & Alex Szimayer, 2008. "GARCH modelling in continuous time for irregularly spaced time series data," Papers 0805.2096, arXiv.org.
    3. Michael Sørensen, 2011. "Prediction-based estimating functions: review and new developments," CREATES Research Papers 2011-05, Department of Economics and Business Economics, Aarhus University.
    4. Michael Sørensen, 2000. "Prediction-based estimating functions," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 123-147.
    5. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
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    Cited by:

    1. Thiago do Rêgo Sousa & Robert Stelzer, 2022. "Moment‐based estimation for the multivariate COGARCH(1,1) process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 681-717, June.
    2. Jingyan Zhang & Jan De Spiegeleer & Wim Schoutens, 2021. "Implied Tail Risk and ESG Ratings," Mathematics, MDPI, vol. 9(14), pages 1-16, July.

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