Unit root in a new Keynesian model

Good day dear all,

Am new to DSGE please forgive me if my questions sound stupid. I developed a sticky price NK DSGE model with inventories and the goal is to estimate the model with and without inventories. Am able to estimate the model when inventories are included. My model without inventories is giving me unit root problem and I did identify that the problem is caused by my real exchange rate equation ( s= s(+1)+ (r-rf)+(infl(+1)-inflf(+1)). I use diffuse_option as suggested in previous discussions but still the model without inventories does not run. I then put a coefficient greater than one on the term (infl(+1)-inflf(+1)) and it works. For example, am able to estimate the model without inventories if I specify the real exchange rate as ( s= s(+1)+ (r-rf)+1.20*(infl(+1)-inflf(+1)). My questions are:


1.) What do I do to fix the unit root problem?
2.) Is it theoretically justifiable to have a coefficient on the inflation term as specified in my second exchange rate equation?

Kind regards

First of all, you need to find out whether this unit root is supposed to be there. Which variables are involved? Does it only affect nominal or also real variables?
And where does this real exchange rate equation come from? Is it a definition or an optimality condition?