Can someone clarify me this.
Consider Xt=0.5+0.8Xt-1+ε MRL=0.5/(1-0.8)=2.5 So if Xt-1 is below this, then Xt will rise towards 2.5 and vice versa. I can’t get the intuition. What if Xt-1 is 68? Then Xt=0.5+0.8*68, which is not even remotely close to 2.5…
Keep going.
I encourage you to put this into Excel and see what happens.
I see what you mean… 
One has to be patient.
Can never be 68, it is a stationary time serie.
It can start at 68 (or anything else, for that matter).
But, no matter where it starts, it will revert to 2.5.
Agree. However a special case because this serie is far far away from its equilibrium (being 68 when it must be 2.5). Wonder what would make that serie to be that far, an incredibly strong exogenous shock, like misinformation for example, or just maybe a new world seeking for equilibrium in the long term.