The “Economic Report to the Pr
The “Economic Report to the President of the United States”included data on the amounts of manufacturers′ new and unfilledorders in millions of dollars. Shown here are the figures for neworders over a 8-year period:
| Year | Order |
| 1 | 54,097 |
| 2 | 54,259 |
| 3 | 55,022 |
| 4 | 55,921 |
| 5 | 62,941 |
| 6 | 64,182 |
| 7 | 72,553 |
| 8 | 76,003 |
Assuming that weights of 5, 3 and 1 are given to the past threeperiods (i.e. a weight of 5 being given to time period t – 1, aweight of 3 being given to time period t – 2, and a weight of 1being given to time period t – 3), what would be the forecasts foryears 4, 5, 6, 7, 8 and 9 using a 3-year weighted moving averagemodel with? What would be the MAD (Mean Absolute Deviation) and MSE(Mean Square Error) for this forecasting model?
Answer:
The weighted moving averages (WMA) forecast, with weights 1, 3and 5 for the nth period is computed using the followingformula:
Forecast period n =(5×Yt−3+3×Yt−2+1×Yt−3)/(5+3+1)= (5×Yt−3+3×Yt−2+1×Yt−3)/9
The 3-month weighted moving average forecasts with weights 1, 3and 5 are calculated in the table below:
Now, the following table shows the calculations of thecorresponding error metrics:
Forecasts for 4, 5, 6, 7, 8, and 9 using a 3-year weightedmoving average model are given in above table under the columnnamed “MA(3) Forecasts”.
MAD = Average of Abs. Error =(1256.1111+7504.3333+4460.8889+9702.5556+7308.3333)/5
MAD = 6046.44
MSE = Average of Error2 =(1577815.1235+56315018.7778+19899529.679+94139584.3086+53411736.1111)/5
MSE = 45068736.8
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