To calculate the weighted moving average forecast for the 4th week using the provided weights (.20, .30, .50) and the values from the previous weeks, you can follow these steps:
-
Identify the time series values for the three preceding weeks:
- Week 1 = 12
- Week 2 = 14
- Week 3 = 15
-
Apply the weights to these values:
- Weight for Week 1 (oldest) = 0.20
- Weight for Week 2 = 0.30
- Weight for Week 3 (most recent) = 0.50
-
Calculate the weighted moving average (WMA) using the formula:
\[ \text{WMA} = (W_1 \times V_1) + (W_2 \times V_2) + (W_3 \times V_3) \]
Where:
- \(V_1\), \(V_2\), and \(V_3\) are the time series values for Week 1, Week 2, and Week 3, respectively.
- \(W_1\), \(W_2\), and \(W_3\) are the corresponding weights.
Now, substitute the values:
\[ \text{WMA} = (0.20 \times 12) + (0.30 \times 14) + (0.50 \times 15) \]
Calculating each term:
- \(0.20 \times 12 = 2.4\)
- \(0.30 \times 14 = 4.2\)
- \(0.50 \times 15 = 7.5\)
Now, add these up:
\[ \text{WMA} = 2.4 + 4.2 + 7.5 = 14.1 \]
Thus, the weighted moving average forecast for the 4th week is 14.1.