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A new hyperbolic GARCH model

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  • Li, Muyi
  • Li, Wai Keung
  • Li, Guodong

Abstract

There are two commonly used hyperbolic GARCH processes, the FIGARCH and HYGARCH processes, in modeling the long-range dependence in volatility. However, the FIGARCH process always has infinite variance, and the HYGARCH model has a more complicated form. This paper builds a simple bridge between a common GARCH model and an integrated GARCH model, and hence a new hyperbolic GARCH model along the lines of FIGARCH models. The new model remedies the drawback of FIGARCH processes by allowing the existence of finite variance as in HYGARCH models, while it has a form nearly as simple as the FIGARCH model. Two inference tools, including the Gaussian QMLE and a portmanteau test for the adequacy of the fitted model, are derived, and an easily implemented test for hyperbolic memory is also constructed. Their finite sample performances are evaluated by simulation experiments, and an empirical example gives further support to our new model.

Suggested Citation

  • Li, Muyi & Li, Wai Keung & Li, Guodong, 2015. "A new hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 189(2), pages 428-436.
    • Handle: RePEc:eee:econom:v:189:y:2015:i:2:p:428-436
    DOI: 10.1016/j.jeconom.2015.03.034
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    Cited by:

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    2. Pan, Qunxing & Li, Peng & Du, Xiuli, 2023. "An improved FIGARCH model with the fractional differencing operator (1-νL)d," Finance Research Letters, Elsevier, vol. 55(PB).
    3. Lanciné Bamba & Ouagnina Hili & Abdou Kâ Diongue & Assi N’Guessan, 2021. "M-Estimate for the stationary hyperbolic GARCH models," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 303-351, December.
    4. Ling, Shiqing & McAleer, Michael & Tong, Howell, 2015. "Frontiers in Time Series and Financial Econometrics: An overview," Journal of Econometrics, Elsevier, vol. 189(2), pages 245-250.
    5. 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.
    6. Klein, Tony & Walther, Thomas, 2017. "Fast fractional differencing in modeling long memory of conditional variance for high-frequency data," Finance Research Letters, Elsevier, vol. 22(C), pages 274-279.
    7. Yanlin Shi, 2021. "Forecasting mortality rates with the adaptive spatial temporal autoregressive model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(3), pages 528-546, April.
    8. 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.
    9. Ling, S. & McAleer, M.J. & Tong, H., 2015. "Frontiers in Time Series and Financial Econometrics," Econometric Institute Research Papers EI 2015-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Dima, Bogdan & Dima, Ştefana Maria, 2017. "Mutual information and persistence in the stochastic volatility of market returns: An emergent market example," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 36-59.

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    More about this item

    Keywords

    ARCH(∞); Hyperbolic GARCH; Long-range dependence; QMLE;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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