Can anyone let me know whether it is possible for an AR(1) time series to have a finite mean-reverting level and at the same time have the absolute value of the lag coefficient being greater than 1?
If it is possible, what are the implication(s), if any? If it is not possible, why not?
It is not possible. If |b1| > 1, then the |xi| --> +∞.
Put some numbers into Excel and try it. You’ll see very quickly.
If it helps your intuition there is a nice image here showing what happens for different values of b1 (denoted as ρ). From top to bottom you have a
A stationary series
A random walk (unit root)
An explosive series (your case)