ascent74 wrote:I am trying to estimate the TAR and MTAR models.

1) However, after reading the docs supplemented with add-in, and previous posts, it is not clear for me, what estimates it provides for above and below treshold.

Logically, I assume that it provides regression of residiuals (saved from long-run regression) to lagged residuals above and below threshold plus to other differenced lagged residiuals. like equation (9) in research? If this is correct, then why do we need exogeneous?

We do not need exogenous variable per se. You may need to control the relationship between endogenous variables (e.g. x1t and x2t). For instance, when modeling the relationship between two emerging market currencies, it is usually wise to use VIX as a regressor (say, z1t). Whether you put exogenous variable(s) into your model, residuals of the long-run equilibrium relationship (equation 2) is of interest here.

ascent74 wrote:Alternatively, does it provide estimates of error correction models? because the add-in provides option to include "exogeneous" variables which influence estimates of ECM model only? like (20, 21).2) Quote from add-in docs: "By design, residuals of the error corection model are used as the treshold series in the analysis". what does it mean?Please, can someone clearly explain for beginner user level thess issues. Many thanks

It means that, if you use exogenous variable(s) in the model, they are evaluated in Eq. 2 (from original study) and that residuals of this equation still refer to disturbance term Mu(t).