Discussions on the spurious hyperbolic memory in the conditional variance and a new model

Kin-Yip Ho, Yanlin Shi

Research output: Contribution to journalArticle


This paper studies the spurious hyperbolic memory in the conditional variance caused by the Markov Regime-Switching GARCH (MRS-GARCH) process. We firstly propose an illustrative cause of this spuriousness and provide simulation evidence. An MRS Hyperbolic GARCH (MRS-HGARCH) model is then developed to successfully address it. Related statistical properties including the stationarity conditions and asymptotic behaviours of the maximum likelihood estimators of the MRS-HGARCH process are also investigated. An empirical study of the S&P 500 and TOPIX indexes returns is then conducted which demonstrates that our MRS-HGARCH model can provide a more reliable estimator of the hyperbolic-memory parameter and outperform both the HGARCH and MRS-GARCH models.

Original languageEnglish
Pages (from-to)83-103
Number of pages21
JournalJournal of Empirical Finance
Publication statusPublished - 1 Jan 2020



  • Hyperbolic GARCH
  • Hyperbolic memory
  • Regime switching
  • Volatility modelling

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