4.9 (a, b) The computations for both the two- and three-month averages appear in the table; the results appear in the figure below.
[pic] (c) MAD (two-month moving average) = .750/10 = .075 MAD (three-month moving average) = .793/9 = .088
Therefore, the two-month moving average seems to have performed better.
|Table for Problem 4.9 (a, b, c) |
| | | |Forecast | ||Error| |
| | |Two-Month |Three-Month |Two-Month |Three-Month |
| |Price per |Moving |Moving |Moving |Moving |
|Month |Chip |Average |Average |Average |Average |
|January |$1.80 | | | | |
|February | 1.67 | | | | |
|March | 1.70 |1.735 | |.035 | |
|April | 1.85 |1.685 |1.723 |.165 |.127 |
|May | 1.90 |1.775 |1.740 |.125 |.160 |
|June | 1.87 |1.875 |1.817 |.005 |.053 |
|July | 1.80 |1.885 |1.873 |.085 |.073 |
|August | 1.83 |1.835 |1.857 |.005 |.027 |
|September | 1.70 |1.815 |1.833 |.115 |.133 |
|October | 1.65 |1.765 |1.777 |.115 |.127 |
|November | 1.70 |1.675 |1.727 |.025 |.027 |
|December | 1.75 |1.675 |1.683 |.075 |.067 |
| | | |Totals |.750| |.793| |
| | | | | | | | |
|4.9 |(d): |
| | | |( = .1 | | |( = .3 | | |( = .5 |
|Month |Price per Chip |Forecast ||Error| |Forecast ||Error| |Forecast ||Error| |
|January |$1.80 |$1.80 |$.00 |$1.80 |$.00 |$1.80 |$.00 |
|February |1.67 |1.80 |.13 | 1.80 | .13 | 1.80 |.13 |
|March |1.70 |1.79 |.09 | 1.76 | .06 | 1.74 |.04 |
|April |1.85 |1.78 |.07 | 1.74 | .11 | 1.72 |.13 |
|May |1.90 |1.79 |.11 | 1.77 | .13 | 1.78 |.12 |
|June |1.87 |1.80 |.07 | 1.81 | .06 | 1.84 |.03 |
|July |1.80 |1.80 |.00 | 1.83 | .03 | 1.86 |.06 |
|August |1.83 |1.80 |.03 | 1.82 | .01 | 1.83 |.00 |
|September |1.70 |1.81 |.11 | 1.82 | .12 | 1.83 |.13 |
|October |1.65 |1.80 |.15 | 1.79 | .14 | 1.76 |.11 |
|November |1.70 |1.78 |.08 | 1.75 | .05 | 1.71 |.01 |
|December |1.75 |1.77 |.02 | 1.73 | .02 | 1.70 |.05 |
| |Totals | |$.86 | | |$.86 | |
( = .5 is preferable, using MAD, to ( = .1 or ( = .3. One could also justify excluding the January error and then dividing by n = 11 to compute the MAD. These numbers would be $.078 (for ( = .1), $.078 (for ( = .3), and $.074 (for ( = .5). 