Suggested Solutions to Assignment 4 (Optional) - Trent University

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