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

• Published in: Journal of empirical finance Vol. 55; pp. 83 - 103
• Main Authors: Ho, Kin-Yip, Shi, Yanlin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2020
• Subjects: Hyperbolic GARCH; Hyperbolic memory; MRS-HGARCH; Regime switching; Volatility modelling; Volatility modelling; C22; ACF; Regime switching; ARFIMA; C58; G32; DGP; MRS; QMLE; Hyperbolic GARCH; Hyperbolic memory; MRS-HGARCH; TRTH; GARCH; BIC; C51
• ISSN: 0927-5398; 1879-1727
• DOI: 10.1016/j.jempfin.2019.11.001

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. •A cause of spurious hyperbolic memory produced by regime switching is proposed.•We incorporate hyperbolic memory and regime switching leading to MRS-HGARCH model.•Our model can effectively address the spurious hyperbolic memory.•Related statistical properties of the new model are presented.•Empirical result suggests it outperforms both the HGARCH and MRS-GARCH models.