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To test the structural breaks and to perform markov-switching model in time series data, should i have stationary data. Thank you in advance.

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In this lecture it is stated at chapter 2.3 that "The Markov switching model and its variants discussed in the preceding sections are only suitable for stationary data". Perhaps you'd like to read into that more thoroughly.

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Since differentiation is allowed, you should also be able to produce an Error-Correcting Model -and its variants- through cointegration if stationarity is not achieved.

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