1.19 Suppose x1, . . . , xn is a sample from the process xt = µ + wt − .8wt−1, where wt ∼ wn(0, σ2 w). (a) Show that mean function is E(xt) = µ. (b) Use XXXXXXXXXXto calculate the standard error of ¯x...

1.19 Suppose x1, . . . , xn is a sample from the process xt = µ + wt − .8wt−1,
where wt ∼ wn(0, σ2
w).
(a) Show that mean function is E(xt) = µ.
(b) Use (1.33) to calculate the standard error of ¯x for estimating µ.
(c) Compare (b) to the case where xt is white noise and show that (b) is
smaller. Explain the result.
1.20 (a) Simulate a series of n = 500 Gaussian white noise observations as in
Example 1.8 and compute the sample ACF, ρb(h), to lag 20. Compare the
sample ACF you obtain to the actual ACF, ρ(h). [Recall Example 1.19.]
(b) Repeat part (a) using only n = 50. How does changing n affect the results?
1.21 (a) Simulate a series of n = 500 moving average observations as in Example 1.9 and compute the sample ACF, ρb(h), to lag 20. Compare the
sample ACF you obtain to the actual ACF, ρ(h). [Recall Example 1.20.]
(b) Repeat part (a) using only n = 50. How does changing n affect the results

need solution for 1.21