One of the well-known class of models that involve a simple difference equation are models of mean reversion. These models typically take the form
yt+1 - yt = -a(yt - μ)where 0 < a< 1
In the equation above μ is the mean of yt.
a) Provide the intuitive explanation for the above equation.
b) Show homogenous, particular and then general solution for the difference equation.
c) Setting t=0 show the solution to the mean-reversion model.
d) Analyze the dynamic path of this model.