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Q1 Proof of Yule-Walker equation
Showing stes to get a Yule-Walker equation of (1) from (2).
(1)
(2)
When observed value X1,….,Xn
. Causal AR(p) process will be obtained.
Hint::
Step 1, You need to multiple Xt-k to both sides of (2)
Step 2, You need to get Expected value from Step1.
Then You will get equation (1) 😉
Q2 Proof of Householder transformation
Residual sum of squares (RSS) is equation (3).
(3) .
As a minimal solution of estimate of (3) is called : least squares estimator…(4)
(4)
Under RSS (3), any Orthogonal matrix( n✖n) of A=[
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