The data set arf is 1000 simulated observations from an ARFIMA(1, 1, 0) model with = .75 and d = .4. (a) Plot the

The data set arf is 1000 simulated observations from an ARFIMA(1, 1, 0)

model with φ = .75 and d = .4.

(a) Plot the data and comment.

(b) Plot the ACF and PACF of the data and comment.

(c) Estimate the parameters and test for the significance of the estimates φb and d b.

(d) Explain why, using the results of parts

(a) and (b), it would seem reasonable to difference the data prior to the analysis. That is, if xt represents the data, explain why we might choose to fit an ARMA model to ∇xt.

(e) Plot the ACF and PACF of ∇xt and comment.

(f) Fit an ARMA model to ∇xt and comment.