Suggested Solutions to Assignment 4 (Optional) - Trent University
Suggested Solutions to Assignment 4 (Optional) - Trent University
Suggested Solutions to Assignment 4 (Optional) - Trent University
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6. (a) The exponential forecasts (F) of new housing starts (A) in the United States for<br />
the years 1986 <strong>to</strong> 1998 with w = 0.3 and w = 0.7 are given in Table 3. They are obtained<br />
by using Equation 6-12 in the text. To get the analysis started, we let F 1986 = 128<br />
(the average of the actual index of housing starts between 1986 and 1997).<br />
(b) From Table 3 we see that F 1998 = 145 with w = 0.3 and 159 with w = 0.7. Since A 1998 = 163,<br />
the exponential forecast with w = 0.7 is better.<br />
With w = 0.3, RMSE = 3 ,369 /12 = 17 and with w = 0.7, RMSE = 1 ,834 /12 = 12 .<br />
Since the RMSE with w = 0.7 is smaller than the RMSE with w = 0.3, the former gives,<br />
on the average, a better forecast.<br />
Table 3<br />
Exponential Forecasts of Index of New-Housing Starts in the United States for 1986–1997<br />
(1)<br />
Year<br />
(2)<br />
A<br />
(3)<br />
F with w = 0.3<br />
(4)<br />
A − F<br />
(5)<br />
(A −F) 2 (6) F<br />
with w = 0.7<br />
(7)<br />
A −F<br />
(8)<br />
(A − F) 2<br />
1986 116 128 −12 144 128 −12 144<br />
1987 122 124 −2 4 120 2 4<br />
1988 121 123 −2 4 121 0 0<br />
1989 121 122 −1 1 121 0 0<br />
1990 111 122 −11 121 121 −10 100<br />
1991 97 119 −22 484 114 −17 281<br />
1992 113 112 1 1 102 11 121<br />
1993 125 112 13 169 110 15 225<br />
1994 146 116 30 900 121 25 625<br />
1995 142 125 17 289 139 3 9<br />
1996 156 130 26 676 141 15 225<br />
1997 162 138 24 576<br />
3,369<br />
1998 145 159<br />
152 10 100<br />
1,834<br />
113