1. Let b(B) = (1 − 0.6B)2(1 + 0.4B) = 1 − 0.8B − 0.12B2 + 0.144B3

(i) Simulate errors for this model with n = 5000 and standard deviation 1.0.

(ii) Plot acf(error) and pacf(error).

(iii) Use ar.yw() or ar.mle() to find the correct order, m, for an AR(m) model and the values ̂a1… ̂am.

(iv) Filter the errors.

(v) Verify, using ar.yw() or ar.mle(), that AR(0) is the model selected for the filtered errors.

(vi) Plot acf(filtered error) and pacf(filtered error).