Score tests for hyperbolic GARCH models

Muyi LI, Guodong LI, Wai Keung LI

Research output: Contribution to journalArticlespeer-review

6 Citations (Scopus)


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. Copyright © 2011 American Statistical Association.
Original languageEnglish
Pages (from-to)579-586
JournalJournal of Business and Economic Statistics
Issue number4
Publication statusPublished - Oct 2011


Li, M., Li, G., & Li, W. K. (2011). Score tests for hyperbolic GARCH models. Journal of Business & Economic Statistics, 29(4), 579-586. doi: 10.1198/jbes.2011.10024


  • Hyperbolic decay
  • Long-range dependence


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