Can we distinguish regime switching from long memory? A simulation evidence

It is well known that long memory can be caused by regime switching and is easily confused with it. However, recent study suggests that if the cause of confusion was properly controlled for, long memory and regime switching could be distinguished. Motivated by this idea, our study aims to distinguish regime switching from long memory for the financial time series. In this article, we model long memory and regime switching via the ARFIMA and Markov regime-switching (MRS) frameworks, respectively. A theoretical proof is provided to show that the time-varying smoothing probability series can induce the presence of significant long memory in the regime-switching process. We then propose a two-stage two-state-ARFIMA (2S-ARFIMA) model to control for the effect of the smoothing probability and use a simulation study to demonstrate that it can effectively distinguish the pure MRS process from the pure ARFIMA process.