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

Abstract

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.

Keywords:

• long memory
• regime switching
• ARFIMA
• Markov regime-switching

JEL Classification:

• C22
• C51

Acknowledgement

The author would like to thank the support of the Research School of Finance, Actuarial Studies and Applied Statistics of the Australian National University.

Notes

¹ Only the mean is allowed to switch between states and the variance is not.

² Since the short memory is not our focus of this article, we ignore the ARMA effects and set both p and q to be 0.

³ In Diebold and Inoue (2001), the confusion between long memory and regime switching is much more significant when transition probabilities are greater than or equal to 0.99. Thus, we only select those transition probabilities in this article.

⁴ p and q are set to 0, since no short memory is allowed to generate the simulations.

⁵ Results are not reported here and are available upon request.

⁶ The smoothed density plots of other sets of the ARFIMA and MRS simulations have the similar shapes as the ARFIMA and MRS examples are presented here, respectively. These plots are not reported in this article and are available upon request.

⁷ We also perform the usual t-test for the MRS DGPs, and the results are consistent with those of the Wilcox sign tests.