ECN 522 Problem Set 9
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ECN 522
Problem Set 9
Due in class by Dec. 5th.
Part 1 Summary
Read Chapter 14-15 and write a minimum two-page summary.
Part 2 Problems
Problem 1
Suppose that Yt follows the stationary AR(1) model,
Yt = 1 + 0:8Yt- 1 + ut
where ut has E[ut] = 0 and V [ut] = 4 and is independent of (Yt 1,Yt 2,Yt 3,...) (and of (ut 1,ut-2,ut-3,...)). Note that the coe¢ cients 1, 0.8 and 4 above are assumed to be known rather than estimated.
(a) Suppose that you observe Yt = 1 and Yt- 1 = 2, what are your forecasts of Yt+1 , Yt+2 and Yt+3?
(b) Compute the mean of Yt.
(c) Compute the variance of Yt
(d) Compute the correlation between Yt and Yt-2 .
(e) What are the root mean squared forecast errors of your forecast of Yt+3 in (a)?
Problem 2
Suppose that Yt follows the stationary AR(2) model,
Yt = -2 + 0.75Yt- 1 - 0:125Yt-2 + ut
where ut has E[ut] = 0 and V [ut] = 9 and is independent of (Yt 1,Yt 2,Yt 3,...) (and of (ut 1,ut-2,ut-3,...)). Note that the coe¢ cients -2, 0.75, -0.125 and 9 above are assumed to be known rather than estimated.
(a) Suppose that you observe Yt = 1 and Yt- 1 = -1, what are your forecasts of Yt+1 and Yt+2 ? (b) Compute the mean of Yt.
(c) What is the root mean squared forecast errors of the forecasts in (a)?
2023-12-06