Q12. Using the model’s results, Briar’s forecast for three years into the future is:

A)   $54.108 million.

B)   $54.543 million.

C)   $47.151 million.

Q13. With respect to the comments of Holmes and Briars concerning the mean reversion of the import data, the long-run mean value that:

A)   Briars computes is correct, but the conclusion is probably not accurate.

B)   Briars computes is correct, and his conclusion is probably accurate.

C)   Briars computes is not correct, but his conclusion is probably accurate.

Q14. Given the output, the most obvious potential problem that Briars and Holmes need to investigate is:

A)   conditional heteroskedasticity.

B)   multicollinearity.

C)   a unit root.

答案和详解如下：

Q12. Using the model’s results, Briar’s forecast for three years into the future is:

A)   $54.108 million.

B)   $54.543 million.

C)   $47.151 million.

Correct answer is A)

Briars’ forecasts for he next three years would be:

year one: 3.8836 + 0.9288 × 54 = 54.0388
year two: 3.8836 + 0.9288 × (54.0388) = 54.0748
year three: 3.8836 + 0.9288 × (54.0748) = 54.1083

Q13. With respect to the comments of Holmes and Briars concerning the mean reversion of the import data, the long-run mean value that:

A)   Briars computes is correct, but the conclusion is probably not accurate.

B)   Briars computes is correct, and his conclusion is probably accurate.

C)   Briars computes is not correct, but his conclusion is probably accurate.

Correct answer is A)

Briars has computed a value that would be correct if the results of the model were reliable. The long-run mean would be 3.8836 / (1 − 0.9288)= 54.5450. However, the evidence suggests that the data is not covariance stationary. The imports have grown steadily from $30 million to $54 million.

Q14. Given the output, the most obvious potential problem that Briars and Holmes need to investigate is:

A)   conditional heteroskedasticity.

B)   multicollinearity.

C)   a unit root.

Correct answer is C)

Multicollinearity cannot be a problem because there is only one independent variable. Although heteroskedasticity may be a problem, nothing in the output provides information in this regard. A unit root is a likely problem because the slope coefficient is so close to one. In fact, if Holmes and Briars divide the t-statistic of the slope coefficient by the value of the coefficient, they could determine the standard error: 0.1032 = 0.9288 / 9.0025. They could then test the null hypothesis:

H₀ : slope coefficient = 1

H₀ : slope coefficient ≠ 1

The t-statistic is:

t = -0.6899 = (0.9288 − 1) / 0.1032

They would not have to go to a t-table to realize that this t-statistic value of -0.6899 is not significant so the hypothesis of the slope equaling one cannot be rejected. Given that serial correlation generally underestimates standard errors, this statistic would become even smaller if that is the case. Finally, the fact that they know that imports have grown from $30 million to $54 million over a 24-year period should provide a clue that the data may have a unit root. Note that this suggests that the true value of the slope also equals one, since with a unit root the dependent variable will grow by approximately the amount of the intercept each year.

thanx