A new hyperbolic GARCH model

Muyi LI, Wai Keung LI, Guodong LI

Research output: Contribution to journalArticlespeer-review

15 Citations (Scopus)


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. Copyright © 2015 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)428-436
JournalJournal of Econometrics
Issue number2
Early online dateMar 2015
Publication statusPublished - Dec 2015


Li, M., Li, W. K., & Li, G. (2015). A new hyperbolic GARCH model. Journal of Econometrics, 189(2), 428-436. doi: 10.1016/j.jeconom.2015.03.034


  • ARCH(∞)
  • Hyperbolic GARCH
  • Long-range dependence
  • QMLE


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