Long memory or regime switching in volatility? Evidence from high-frequency returns on the U.S. stock indices

Recent research suggests that long memory and regime switching can be effectively distinguished, if the cause of the confusion between them is properly controlled for. Motivated by this idea, our study aims to distinguish between them in modelling stock return volatility. We firstly model long memory and regime switching in volatility via the Long-Memory GARCH (LMGARCH) and Markov Regime-Switching GARCH (MRS-GARCH) models, respectively. A theoretical cause of the confusion between those processes is proposed with simulation evidence. Adopting the ideas of existing studies, an MRS-LMGARCH framework is further developed to control for this cause. Our Monte Carlo studies show that this model can effectively distinguish between the pure LMGARCH and pure MRS-GARCH processes. Finally, empirical studies of NASDAQ and S&P 500 index returns are conducted to demonstrate that our MRS-LMGARCH model can provide potentially more reliable estimates of the long-memory parameter, identify the volatility states and outperform both the LMGARCH and MRS-GARCH models.