Let Yt be a stationary AR(2) process, (Yt- μ) = Ï1(Yt-1 - μ) + Ï2(Yt-2 - μ)
Question:
(Yt- μ) = Ï1(Yt-1 - μ) + Ï2(Yt-2 - μ) + t.
(a) Show that the ACF of Yt satisfies the equation
p(k) = Ï1p(k - 1) + Ï2p(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 (Ï1, Ï2) solves the following system of equations:
(c) Suppose that p(1) = 0.4 and p(2) = 0.2. Find Ï1, Ï2, and p(3).
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Related Book For
Statistics And Data Analysis For Financial Engineering
ISBN: 9781461427490
1st Edition
Authors: David Ruppert
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