Long Memory and Regime Switching in the Second Moment: A Simulation Study

Abstract

This paper studies the confusion between the Hyperbolic GARCH (HGARCH) and Markov Regime-Switching GARCH (MRS-GARCH) processes. We firstly propose the cause of this confusion and provide simulation evidence. An MRS-HGARCH model is then developed to address the confusion. Our Monte Carlo studies demonstrate that this model can effectively distinguish between the pure HGARCH and pure MRS-GARCH processes. When the proposed model is further employed to fit simulations containing both hyperbolic memory and regime switching, it outperforms the ordinary HGARCH model. Moreover, the related statistical properties including the asymptotic behaviours of the maximum likelihood estimators of the MRS-HGARCH process are briefly investigated. Finally, an empirical study of the S\&P 500 index return is 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.