Sebastian, I would use a Markov Switching Model and let the model find endogenously the threshold unless this is defined exogenously (by policymakers, regulations, etc). Hamilton is the best reference to do that. Giraldo, Misas and Villa (2012, 2014) use that econometric method in the framework of Taylor Rules.

You may also explore Bai and Perron method of dealing with multiple structural breaks. These breaks may be exogenously or endogenously determined. In your case, those breaks would be the threshold(s).

Another estimation method is the regression discontinuity. Mastering Metrics by Angrist and Pischke explains the method. In this case, the threshold is predetermined. I do not know if your economic model adjusts to this method but it would be an interesting macro  question answered by using a microeconometric method.

Hope this answer is useful. Best regards!

Sir,

I don't know the exact deviation that can be caused by the variable Xt. We have to note that the dependent and independent variables only will not play the whole equation, while some extraneous variables will also vitally plays. I have added a link through which optimization could be understood with examples and can be made. I will also search for some econometric models that suits our problem to solve. Only more of forecasts and trends will be dealt in by the econometric.

Thank you.

http://www.fq.math.ca/Scanned/36-3/tang.pdf

Markov  switching  models,  and  smooth  transition  threshold models

You should use TAR or STAR models. If you think your regime change happens "suddenly" use TAR, smooth changes modelled with STAR.

You may refer to van Dijk's “Smooth Transition Autoregressive Models-A Survey of Recent Developments” article for details.

of course you can use either  Markov switching models, and smooth transition threshold models, However If I were you I will use STTM  as the change in your breaks ( Liquidity levels happens slowly)

I suggest you running Markov Swithing Model that is proper for your case.

https://www.mdpi.com/2225-1146/7/2/23/htm