Using i. Find the values for , and . 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...

Using

i. Find the values for
, and
.

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).