For the following general AR(2) process, Xt = 1Xt1 + 2Xt2 + et write down the characteristic equation; plug in the appropriate s into the

For the following general AR(2) process, Xt = β1Xt−1 + β2Xt−2 + et write down the characteristic equation; plug in the appropriate βs into the quadratic formula to describe its roots. Write down the inverse characteristic equation; plug in the appropriate βs into the quadratic formula to describe its roots. Show that the two roots are reciprocals of each other. (Hint: Reciprocals multiply to one.)