Consider the AR(3) model i. Find , and . ii. Simulate errors for this model with n = 400 and σ = 2.5. iii. Construct a filtering matrix A using , and . iv. Filter the errors and use pacf() and...

Consider the AR(3) model

i. Find

,

and

.

ii. Simulate errors for this model with n = 400 and σ = 2.5.

iii. Construct a filtering matrix A using

,

and

.

iv. Filter the errors and use pacf() and ar.yw() [ or ar.mle()] to demonstrate the filtering has been successful.