Forecasting. You have the following data in Table 2:

Table 2

Year and quarter Gasoline Sales

1995.1 22434

1995.2 23766

1995.3 23860

1995.4 23391

1996.1 22662

1996.2 24032

1996.3 24171

1996.4 23803

1997.1 22776

1997.2 24491

1997.3 24751

1997.4 24170

1998.1 23302

1998.2 24045

1998.3 25437

1998.4 25272

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A.Using data on gasoline sales (in thousands of barrels) from the first quarter of 1995 to the last quarter of 1998, the following trend line equation was estimated:

Regressing gasoline sales(St) on time, from t=1 from the first quarter of 1995 to t = 16 for the last quarter of 1998, we got:

St =22,902.05+ 117.06 t R squire = 0.42

(36.83)

Use the estimated line trend equation to forecast gasoline sales in each quarter of 1999.

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B. Use the log-linear trend equation below to forecast gasoline sales in each quarter of 1999.

Regressing the logarithm of gasoline sales (Ln St) on time, from t=1 for the first quarter1995 to t = 16 for the last quarter 1998, we get:

Ln St = 10.04 +0.0049t R square =0.41

(3.15)

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C. Based on the results in sections A and B above, which form of the trend fits the historical data better? Why would we expect both forecasts to be rather poor?

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D. Forecasting: Seasonal Adjustment. Based on the data in Table 2 above:

(i)Adjust the linear trend projection found in section A. above for the seasonal variation in the data using the ratio-to-trend method.

(ii)We regressed the original data using dummy variables to adjust for seasonal variation. Taking the last quarter as the base-period quarter, and defining dummy variable D1 by a time series with ones in the first quarter of each year and zero in other quarters; D2 by a time series with ones in the second quarter of each year and zero in other quarters; and D3 by a time series with ones in the third quarter and zero in other quarters, we obtain the following results by running a regression of gasoline sales on seasonal dummy variables and the linear time trend:

St = 23,201.19 - 1,080.66D1t + 116.06D2t + 491.53 D3t + 95.78t R square = 0.90

(-4.61) (0.50) (2.15) (5.31)

Note that the estimated coefficients for the dummy variables and the trend variable are all statistically significant at better than the 5% significance level except for D_2t, and that the regression explains almost 90% of the variation in gasoline sales (as compared with only 41% for the regression in section B above).

Your job is to adjust the linear trend projection found in (section A. above) using the regression equation based on dummy variables.

Dear

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