This paper explores the relationship between long memory and regime switching, arguing that these two phenomena are closely related and can be easily confused, especially when only a small amount of regime switching occurs. The authors provide theoretical analysis and Monte Carlo simulations to support their claims. They consider several models, including a simple mixture model, Engle and Lee’s stochastic permanent break model, and Hamilton’s Markov switching model. The results show that under certain conditions, these models can exhibit long memory behavior, leading to potential confusion with structural change. The Monte Carlo experiments further demonstrate the finite-sample inference implications of these models, highlighting the practical significance of the theoretical findings. The paper concludes by discussing the implications of these results and their relationship to recent related work in the literature.This paper explores the relationship between long memory and regime switching, arguing that these two phenomena are closely related and can be easily confused, especially when only a small amount of regime switching occurs. The authors provide theoretical analysis and Monte Carlo simulations to support their claims. They consider several models, including a simple mixture model, Engle and Lee’s stochastic permanent break model, and Hamilton’s Markov switching model. The results show that under certain conditions, these models can exhibit long memory behavior, leading to potential confusion with structural change. The Monte Carlo experiments further demonstrate the finite-sample inference implications of these models, highlighting the practical significance of the theoretical findings. The paper concludes by discussing the implications of these results and their relationship to recent related work in the literature.