Let Yt be a stationary AR(2) process, (a) Show that the ACF of Yt satisfies the equation for all values of k > 0. (These are a special case of the Yule–Walker equations.) (b) Use part (a) to show that...

Let Yt be a stationary AR(2) process,

(a) Show that the ACF of Yt satisfies the equation

for all values of k > 0. (These are a special case of the Yule–Walker equations.)

(b) Use part (a) to show that (φ1, φ2) solves the following system of equations: