To calculate the absolute error for each forecast using the four-period simple moving average, we take the absolute difference between the actual demand and the forecasted demand for each period where a forecast can be made.

### Four-Period Simple Moving Average Absolute Errors

For the four-period moving average, we begin calculating forecasts starting from period 5. Below are the absolute errors for each forecasted period:

1. **Period 5**:
   \[
   \text{Absolute Error} = |106 - 129.50| = 23.50
   \]

2. **Period 6**:
   \[
   \text{Absolute Error} = |101 - 124.50| = 23.50
   \]

3. **Period 7**:
   \[
   \text{Absolute Error} = |132 - 121.75| = 10.25
   \]

4. **Period 8**:
   \[
   \text{Absolute Error} = |141 - 121.00| = 20.00
   \]

5. **Period 9**:
   \[
   \text{Absolute Error} = |110 - 120.00| = 10.00
   \]

6. **Period 10**:
   \[
   \text{Absolute Error} = |133 - 121.00| = 12.00
   \]

### Summary of Absolute Errors

- **Period 5**: 23.50
- **Period 6**: 23.50
- **Period 7**: 10.25
- **Period 8**: 20.00
- **Period 9**: 10.00
- **Period 10**: 12.00

These values show the magnitude of the forecasting errors for each period when using a four-period moving average.

### Questions for Further Exploration

1. What patterns can be observed from the absolute errors of the four-period moving average?
2. How would the absolute errors change if we used a different number of periods for the moving average?
3. Why might a moving average model underperform in periods with significant demand shifts?
4. How can visualizing absolute errors help in assessing the forecasting model's performance?
5. What steps can be taken to improve forecast accuracy when using moving averages?
6. Can you discuss the impact of increasing the moving average period on the sensitivity to changes in demand?
7. How does the choice of a four-period moving average affect the smoothing of the data?
8. How can absolute errors be used to calculate other error metrics, such as mean squared error?

### Tip

To better understand the performance of a forecasting model, consider using multiple error metrics like Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) alongside MAD. These metrics provide different insights into the forecast accuracy and can help identify trends or biases in the model.

Learn how to calculate the absolute error for each forecast using the four-period simple moving average. This problem demonstrates the application of forecasting techniques in real-world scenarios. Includes step-by-step calculations and insights into forecasting accuracy.

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