To calculate the weighted moving average (WMA) forecast for the 4th week using the weights provided, we'll be using the time series values from the past three weeks (Week 2, Week 3, and Week 4) since WMA takes into account the most recent data points with specific weights.
The weights are as follows:
- Week 2: 0.20
- Week 3: 0.30
- Week 4: 0.50
Now we'll apply the WMA formula:
\[ \text{WMA} = (W_1 \times V_1) + (W_2 \times V_2) + (W_3 \times V_3) \]
Where:
- \( W_1, W_2, W_3 \) are the weights for weeks 2, 3, and 4 respectively.
- \( V_1, V_2, V_3 \) are the corresponding time series values for those weeks.
Using the values:
- For Week 2 (V_1 = 19.00): \( W_1 = 0.20 \)
- For Week 3 (V_2 = 15.00): \( W_2 = 0.30 \)
- For Week 4 (V_3 = 17.00): \( W_3 = 0.50 \)
Now substituting these into the formula:
\[ \text{WMA} = (0.20 \times 19.00) + (0.30 \times 15.00) + (0.50 \times 17.00) \]
Calculating each term:
- \( 0.20 \times 19.00 = 3.80 \)
- \( 0.30 \times 15.00 = 4.50 \)
- \( 0.50 \times 17.00 = 8.50 \)
Adding these together:
\[ \text{WMA} = 3.80 + 4.50 + 8.50 = 16.80 \]
Thus, the weighted moving average forecast for the 4th week is 16.80.