4. Consider the AR(3) model

(1 − 0.7B)(1 − [0.4 − 0.1i]B)(1 − [0.4 + 0.1i]B)????n = wn:

(i) Find a1, a2 and a3.

(ii) Simulate errors for this model with n = 400 and ???? = 2.5.

(iii) Construct a filtering matrix A using a1, a2, and a3.

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