6.sed 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 two equations are equally useful in explaining warranty expense.
B) the provided results are not sufficient to reach a conclusion.
C) the trend model has more explanatory power for warranty expense.
D) the autoregressive model on the first differenced data has more explanatory power for warranty expense.
7.sed on the autoregressive model, expected warranty expense in the first quarter of 2005 will be closest to:
A) $60 million.
B) $71 million.
C) $65 million.
D) $78 million.
8.sed upon the results, is there a seasonality component in the data?
A) Yes, because the coefficient on yt-4 is large compared to its standard error.
B) No, because the slope coefficients in the autoregressive model have opposite signs.
C) No, because one of the slope coefficient estimates is not significant.
D) Yes, because the coefficient on yt is small compared to its standard error.
9.llier most likely chose to use first-differenced data in the autoregressive model:
A) in order to avoid problems associated with unit roots.
B) because the time trend was significant.
C) to increase the explanatory power.
D) to increase the degrees of freedom.
10.sider the following estimated model:
(Salest - Sales t-1)= 100 - 1.5 (Sales t-1 - Sales t-2) + 1.2 (Sales t-4 - Sales t-5) t=1,2,.. T
and Sales for the periods 1999.1 through 2000.2:
t | Period | Sales |
T | 2000.2 | $1,000 |
T-1 | 2000.1 | $900 |
T-2 | 1999.4 | $1,200 |
T-3 | 1999.3 | $1,400 |
T-4 | 1999.2 | $1,000 |
T-5 | 1999.1 | $800 |
The forecasted Sales amount for 2000.3 is closest to:
A) $1,430.
B) $1,730.
C) $370.
D) $730.
6.sed 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 two equations are equally useful in explaining warranty expense.
B) the provided results are not sufficient to reach a conclusion.
C) the trend model has more explanatory power for warranty expense.
D) the autoregressive model on the first differenced data has more explanatory power for warranty expense.
The correct answer was 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.
7.sed on the autoregressive model, expected warranty expense in the first quarter of 2005 will be closest to:
A) $60 million.
B) $71 million.
C) $65 million.
D) $78 million.
The correct answer was C)
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.
8.sed upon the results, is there a seasonality component in the data?
A) Yes, because the coefficient on yt-4 is large compared to its standard error.
B) No, because the slope coefficients in the autoregressive model have opposite signs.
C) No, because one of the slope coefficient estimates is not significant.
D) Yes, because the coefficient on yt is small compared to its standard error.
The correct answer was A)
The coefficient on the 4th lag tests the seasonality component. The t-ratio is 44.6. Even using Chebychev’s inequality, this would be significant. None of the other answers are correct or relate to the seasonality of the data.
9.llier most likely chose to use first-differenced data in the autoregressive model:
A) in order to avoid problems associated with unit roots.
B) because the time trend was significant.
C) to increase the explanatory power.
D) to increase the degrees of freedom.
The correct answer was A)
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. First-differencing data will lower the degrees of freedom because an observation is lost in the creation of the series. The time trend was not significant, so that was not a possible answer.
10.sider the following estimated model:
(Salest - Sales t-1)= 100 - 1.5 (Sales t-1 - Sales t-2) + 1.2 (Sales t-4 - Sales t-5) t=1,2,.. T
and Sales for the periods 1999.1 through 2000.2:
t | Period | Sales |
T | 2000.2 | $1,000 |
T-1 | 2000.1 | $900 |
T-2 | 1999.4 | $1,200 |
T-3 | 1999.3 | $1,400 |
T-4 | 1999.2 | $1,000 |
T-5 | 1999.1 | $800 |
The forecasted Sales amount for 2000.3 is closest to:
A) $1,430.
B) $1,730.
C) $370.
D) $730.
The correct answer was A)
Change in sales = $100 - 1.5 ($1,000-900) + 1.2 ($1,400-1,000)
Change in sales = $100 - 150 + 480 =$430
Sales = $1,000 + 430 = $1,430
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