Question

The “Economic Report to the President of the United States” included data on the amounts of manufacturers′ new and unfilled orders in millions of dollars. Shown here are the figures for new orders 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 three periods (i.e. a weight of 5 being given to time period t – 1, a weight of 3 being given to time period t – 2, and a weight of 1 being given to time period t – 3), what would be the forecasts for years 4, 5, 6, 7, 8 and 9 using a 3-year weighted moving average model with? What would be the MAD (Mean Absolute Deviation) and MSE (Mean Square Error) for this forecasting model?

Answer 1

The weighted moving averages (WMA) forecast, with weights 1, 3 and 5 for the n^th period is computed using the following formula:

Forecast period n = (5×Y_t−3​+3×Y_t−2​+1×Y_t−3​​)/(5+3+1) = (5×Y_t−3​+3×Y_t−2​+1×Y_t−3​​)/9

The 3-month weighted moving average forecasts with weights 1, 3 and 5 are calculated in the table below:

Now, the following table shows the calculations of the corresponding error metrics:

Forecasts for 4, 5, 6, 7, 8, and 9 using a 3-year weighted moving average model are given in above table under the column named "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