Suggested Solutions to Assignment 4 (Optional) - Trent University

More documents

Recommendations

Info

Table 2 Number of New-Housing Starts in the United States in Each Year, 2005–2009 (in thousands of units) Year New-Housing Starts 2005 2,068.3 2006 1,800.9 2007 1,355.0 2008 905.5 2009 553.8 5. Since the problem asks to forecast the index of new housing starts for 1998 and compare it to the index of 163 already known, we only forecast the index for 1998 without the need to forecast the index for all previous years. The only reason for forecasting all previous years would be to calculate the root-meansquare error (RMSE) of the forecast obtained with different moving averages so as to be able to choose the forecast of the moving average with the smallest RMSE. Since we know here the actual value of the index for 1998, we can compare our results directly with the actual index rather than using RMSE. The three-year moving average index of new housing starts in the United States for 1998 is obtained by summing the indexes from 1995, 1996, and 1997 and dividing by 3. This is (142 + 156 + 162)/3 = 460/3 = 153.3 or 153. On the other hand, the five-year moving average is obtained by summing the indexes for the five years from 1993 to 1997 and dividing by 5. This is (125 + 146 + 142 + 156 + 162)/5 = 731/5 = 146.2 or 146. Neither the three-year nor the five-year moving average provides a good forecast for the actual index of 163 for 1998, but the three-year moving average is somewhat better. In fact, the RMSE for the three-year moving average is 17, while the RMSE for the five-year moving average is 24. 112
6. (a) The exponential forecasts (F) of new housing starts (A) in the United States for the years 1986 to 1998 with w = 0.3 and w = 0.7 are given in Table 3. They are obtained by using Equation 6-12 in the text. To get the analysis started, we let F 1986 = 128 (the average of the actual index of housing starts between 1986 and 1997). (b) From Table 3 we see that F 1998 = 145 with w = 0.3 and 159 with w = 0.7. Since A 1998 = 163, the exponential forecast with w = 0.7 is better. With w = 0.3, RMSE = 3 ,369 /12 = 17 and with w = 0.7, RMSE = 1 ,834 /12 = 12 . Since the RMSE with w = 0.7 is smaller than the RMSE with w = 0.3, the former gives, on the average, a better forecast. Table 3 Exponential Forecasts of Index of New-Housing Starts in the United States for 1986–1997 (1) Year (2) A (3) F with w = 0.3 (4) A − F (5) (A −F) 2 (6) F with w = 0.7 (7) A −F (8) (A − F) 2 1986 116 128 −12 144 128 −12 144 1987 122 124 −2 4 120 2 4 1988 121 123 −2 4 121 0 0 1989 121 122 −1 1 121 0 0 1990 111 122 −11 121 121 −10 100 1991 97 119 −22 484 114 −17 281 1992 113 112 1 1 102 11 121 1993 125 112 13 169 110 15 225 1994 146 116 30 900 121 25 625 1995 142 125 17 289 139 3 9 1996 156 130 26 676 141 15 225 1997 162 138 24 576 3,369 1998 145 159 152 10 100 1,834 113
Page 1: ECON 3400H Managerial Economics Ins
Page 5 and 6: (c) Time series C is a lagging indi
Page 7 and 8: 14. (a) Wait for June 2012 when the
Page 9: ln Q 61 = 1.2789 − 0.1647(0.47) +

Suggested Solutions to Assignment 4 (Optional) - Trent University

Create successful ePaper yourself

Delete template?

Save as template?