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Score Tests for Hyperbolic GARCH Models

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  • Muyi Li
  • Guodong Li
  • Wai Keung Li

Abstract

Davidson (2004) recently proposed the hyperbolic GARCH model to capture the phenomenon of long-range dependence in volatility, with the extent of such dependence measured by the geometric or hyperbolic decay of the coefficients in an ARCH(∞) model. In this article, we reinterpret the hyperbolic GARCH model by building a link with the common GARCH model, and construct a simplified score test to check the presence of the hyperbolic decay. We derive the asymptotic of the test statistic under the null hypothesis and the local alternatives. We conduct Monte Carlo simulation experiments to study the performance of this test, and report an illustration on two log return sequences. This article has supplementary material online.

Suggested Citation

  • Muyi Li & Guodong Li & Wai Keung Li, 2011. "Score Tests for Hyperbolic GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 579-586, October.
    • Handle: RePEc:taf:jnlbes:v:29:y:2011:i:4:p:579-586
    DOI: 10.1198/jbes.2011.10024
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    Cited by:

    1. Li, Muyi & Li, Wai Keung & Li, Guodong, 2015. "A new hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 189(2), pages 428-436.
    2. Toktam Valizadeh & Saeid Rezakhah & Ferdous Mohammadi Basatini, 2021. "On time‐varying amplitude HGARCH model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2538-2547, April.
    3. Christian Conrad & Melanie Schienle, 2020. "Testing for an Omitted Multiplicative Long-Term Component in GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 229-242, April.
    4. repec:wyi:journl:002190 is not listed on IDEAS
    5. Muyi Li & Wai Keung Li & Guodong Li, 2013. "On Mixture Memory Garch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 606-624, November.
    6. Heitham Al-Hajieh, 2017. "Evaluated the Success of Fractionally Integrated-GARCH Models on Prediction Stock Market Return Volatility in Gulf Arab Stock Markets," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 9(7), pages 200-213, July.

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