Given the following historical data and weights of .5, .3 and .2, what is the three-period weighted moving average forecast for period 5?

Period Value

1

138
2 142
3 148
4 144

Question

Given the following historical data and weights of .5, .3 and .2, what is the three-period weighted moving average forecast for period 5?

Period	Value

1

138
2	142
3	148
4	144

BlackTom AI · Accepted Answer

Step into the problem by identifying what is being forecasted: a three-period weighted moving average for period 5 using the weights 0.5, 0.3, and 0.2.

First, determine which historical values feed into the forecast for period 5. With a three-period moving average, the forecast for period 5 uses the actual values from periods 4, 3, and 2, in that order, weighted by the given weights.

Compute the forecast using the weighted sum:
- 0.5 × Value in period 4 = 0.5 × 144 = 72
- 0.3 × Value in period 3 = 0.3 × 148 = 44.4
- 0.2 × Value in period 2 = 0.2 × 142 = 28.4
- Total forecast for period 5 = 72 + 44.4 + 28.4 = 144.8

Now evaluate the answer options one by one to see why they are or aren’t correct:

Option A: 144.67
This value would imply a different weighting or different past values. If you tried to reconstruct it, it wouldn’t match 0.5·144 + 0.3·148 + 0.2·142, so it’s not consistent with the given weights and data.

Option B: 144
A forecast of 144 would require a sum of weighted components equal to 144. However, the exact weighted sum computed above is 144.8, so 144 is not correct.

Option C: 144.20
This is close to 144.8 but still missing 0.6. It could arise from misplacing a decimal or altering one weight, but with the stated weights (0.5, 0.3, 0.2) and the specified period values, the precise calculation does not yield 144.20.

Option D: 144.80
This matches the exact weighted sum calculated: 72 + 44.4 + 28.4 = 144.8. Since the weights sum to 1 and we used periods 4, 3, and 2 in order with the correct coefficients, this is the correct weighted moving average forecast for period 5.

Option E: 143
A forecast of 143 would correspond to a substantial deviation from the computed weighted sum, indicating an incorrect application of weights or the use of different past periods. With the given data, this value does not align with 0.5, 0.3, and 0.2 applied to 144, 148, and 142 respectively.

In summary, by applying the weights 0.5, 0.3, and 0.2 to periods 4, 3, and 2 respectively, the precise calculation yields 144.8, which corresponds to the option 144.80.

Given the following historical data and weights of .5, .3 and .2, what is the three-period weighted moving average forecast for period 5? Period Value 1 138 2 142 3 148 4 144

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