Can Markov switching model generate long memory?

In an influential work by Diebold and Inoue (2001), the Markov switching model was shown to exhibit long memory, in terms of the behavior of the second moments of partial sums. The relationship between the Markov switching model and long memory is reexamined here. Common estimators of the long memory parameter are found to be extremely biased when applied to the data generated by the Markov switching model. An explanation for these findings is provided.