8. Using (1 − .7B)(1 + [0.1 − 0.1i]B)(1 − [0.1 + 0.1i]B)????n = wn

(i) Find the values for a1, a2, and a3.

(ii) Why do we know this is a stationary process?

(iii) Write out the Yule–Walker equations for AR(3).

(iv) Simulate n = 500 observations from this model.

(v) Using ar.yw() [or ar.mle()] and pacf(), assess whether the data appears to be AR(3).

(vi) Using ar.yw(x, aic = FALSE, order.max = 3) verify that the values computed with this routine satisfy the Yule–Walker equations (expect an unavoidable round-off error on your part).