Let Yt be a stationary AR(2) process, (Yt- μ) = Ï1(Yt-1 - μ) + Ï2(Yt-2 - μ) + t. (a) Show that the ACF of

Let Yt be a stationary AR(2) process,
(Yt- μ) = Ï•1(Yt-1 - μ) + Ï•2(Yt-2 - μ) + ˆˆt.
(a) Show that the ACF of Yt satisfies the equation
p(k) = Ï•1p(k - 1) + Ï•2p(k - 2)
for all values of k > 0. (These are a special case of the Yule-Walker equations.)
(b) Use part (a) to show that (Ï•1, Ï•2) solves the following system of equations:

(c) Suppose that p(1) = 0.4 and p(2) = 0.2. Find Ï•1, Ï•2, and p(3).

p(2)