To calculate the 2-period moving average, we take the average of the time series values for the two preceding weeks.
Step 1: Calculate the 2-period moving average for each week
- Week 1: No moving average can be calculated as there is no data from the previous week.
- Week 2: No moving average can be calculated as there is only one previous value (Week 1).
- Week 3: \( \text{Moving Average} = \frac{\text{Week 1 Value} + \text{Week 2 Value}}{2} = \frac{5 + 6}{2} = \frac{11}{2} = 5.5 \)
- Week 4: \( \text{Moving Average} = \frac{\text{Week 2 Value} + \text{Week 3 Value}}{2} = \frac{6 + 21}{2} = \frac{27}{2} = 13.5 \)
Step 2: Forecast for Week 4 using 2-period moving average
The forecast for Week 4 is 13.5.
Step 3: Calculate the absolute error for Week 4
The absolute error is calculated as the absolute difference between the actual value and the forecasted value:
- Actual Value for Week 4: 6
- Forecasted Value for Week 4: 13.5
\[ \text{Absolute Error} = | \text{Actual Value} - \text{Forecasted Value} | = | 6 - 13.5 | = |-7.5| = 7.5 \]
Summary
- 2-Period Moving Average Forecast for Week 4: 13.5
- Absolute Error for Week 4: 7.5