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I´m currently dealing with threshold VECM models in time series. The basic idea behind a TVECM, according to Lo and Zivot 2001 is

TVECM

There is one point I don´t understand: As far as I see every coefficient is regime specific (including beta). So shouldn´t it be possible to just split the sample between the two regimes and estimate two separate normal VECMs? (I´m pretty sure that is wrong but I can´t find an proper explanation for this)

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