Q5. The mean reverting level for the first equation is closest to:

A)   -0.8.

B)   20.0.

C)   43.6.

Q6. Based upon the output provided by Collier to his supervisor and without any further calculations, in a comparison of the two equations’ explanatory power of warranty expense it can be concluded that:

A)   the autoregressive model on the first differenced data has more explanatory power for warranty expense.

B)   the provided results are not sufficient to reach a conclusion.

C)   the two equations are equally useful in explaining warranty expense.

Q7. Based on the autoregressive model, expected warranty expense in the first quarter of 2005 will be closest to:

A)   $78 million.

B)   $65 million.

C)   $60 million.

Q8. Based upon the results, is there a seasonality component in the data?

A)   No, because the slope coefficients in the autoregressive model have opposite signs.

B)   Yes, because the coefficient on y_t is small compared to its standard error.

C)   Yes, because the coefficient on y_t-4 is large compared to its standard error.

Q9. Collier most likely chose to use first-differenced data in the autoregressive model:

A)   to increase the explanatory power.

B)   in order to avoid problems associated with unit roots.

C)   because the time trend was significant.

答案和详解如下：

Q5. The mean reverting level for the first equation is closest to:

A)   -0.8.

B)   20.0.

C)   43.6.

Correct answer is B)

The mean reverting level is X₁ = b_o/(1-b₁)

X₁ = 74.1/[1-(-2.7)] = 20.03

Q6. Based upon the output provided by Collier to his supervisor and without any further calculations, in a comparison of the two equations’ explanatory power of warranty expense it can be concluded that:

A)   the autoregressive model on the first differenced data has more explanatory power for warranty expense.

B)   the provided results are not sufficient to reach a conclusion.

C)   the two equations are equally useful in explaining warranty expense.

Correct answer is B)

Although the R-squared values would suggest that the autoregressive model has more explanatory power, there are a few problems. First, the models have different sample periods and different numbers of explanatory variables. Second, the actual input data is different. To assess the explanatory power of warranty expense, as opposed to the first differenced values, we must transform the fitted values of the first-differenced data back to the original level data to assess the explanatory power for the warranty expense.

Q7. Based on the autoregressive model, expected warranty expense in the first quarter of 2005 will be closest to:

A)   $78 million.

B)   $65 million.

C)   $60 million.

Correct answer is B)

Substituting the 1-period lagged data from 2004.4 and the 4-period lagged data from 2004.1 into the model formula, change in warranty expense is predicted to be higher than 2004.4.

11.73 =-0.7 - 0.07*24+ 0.83*17.

The expected warranty expense is (53 + 11.73) = $64.73 million.

Q8. Based upon the results, is there a seasonality component in the data?

A)   No, because the slope coefficients in the autoregressive model have opposite signs.

B)   Yes, because the coefficient on y_t is small compared to its standard error.

C)   Yes, because the coefficient on y_t-4 is large compared to its standard error.

Correct answer is C)

The coefficient on the 4^th lag tests the seasonality component. The t-ratio is 44.6. Even using Chebychev’s inequality, this would be significant. Neither of the other answers are correct or relate to the seasonality of the data.

Q9. Collier most likely chose to use first-differenced data in the autoregressive model:

A)   to increase the explanatory power.

B)   in order to avoid problems associated with unit roots.

C)   because the time trend was significant.

Correct answer is B)

Time series with unit roots are very common in economic and financial models, and unit roots cause problems in assessing the model. Fortunately, a time series with a unit root may be transformed to achieve covariance stationarity using the first-differencing process. Although the explanatory power of the model was high (but note the small sample size), a model using first-differenced data often has less explanatory power. The time trend was not significant, so that was not a possible answer.

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