Let's tackle each part of the problem step by step using the provided time series data. We'll start by computing the six-period simple moving average, then calculate the Mean Absolute Deviation (MAD), forecast the demand for period 11, and finally compute the error associated with the forecast.

a. Compute all possible forecasts using a six-period simple moving average model.

The six-period simple moving average is calculated by averaging the demand values of the last six periods. For example, the forecast for period 7 is the average of the demands from periods 1 to 6.

Here’s the calculation:

$\text{Forecast for period 7} = \frac{130 + 122 + 121 + 116 + 141 + 105}{6}$

Let's compute the forecasts for all possible periods.

$\text{Forecast for period 7} = \frac{130 + 122 + 121 + 116 + 141 + 105}{6} = 122.5$ $\text{Forecast for period 8} = \frac{122 + 121 + 116 + 141 + 105 + 116}{6} = 120.2$ $\text{Forecast for period 9} = \frac{121 + 116 + 141 + 105 + 116 + 118}{6} = 119.5$ $\text{Forecast for period 10} = \frac{116 + 141 + 105 + 116 + 118 + 142}{6} = 123.0$

b. Compute the MAD (Mean Absolute Deviation).

MAD is calculated as the average of the absolute deviations between the actual demand and the forecasted demand. We will compute the deviations for the periods where we have forecasts and then find the mean.

$\text{Deviation for period 7} = |116 - 122.5| = 6.5$ $\text{Deviation for period 8} = |118 - 120.2| = 2.2$ $\text{Deviation for period 9} = |142 - 119.5| = 22.5$ $\text{Deviation for period 10} = |125 - 123.0| = 2.0$

Now, let's compute the MAD:

$\text{MAD} = \frac{6.5 + 2.2 + 22.5 + 2.0}{4} = 8.3$

c. What is the forecast demand for period 11?

To forecast period 11, we will use the average of the demands from periods 5 to 10:

$\text{Forecast for period 11} = \frac{141 + 105 + 116 + 118 + 142 + 125}{6} = 124.5$

d. What is the error associated with the eleventh-period forecast?

Since we don't have the actual demand for period 11, the error cannot be computed directly without this information. However, if the actual demand for period 11 is known, the error would be calculated as:

$\text{Error} = \text{Actual Demand for Period 11} - \text{Forecasted Demand for Period 11}$

Summary of Results:

1. Forecasts using a six-period simple moving average model:
   • Period 7: 122.5
   • Period 8: 120.2
   • Period 9: 119.5
   • Period 10: 123.0
2. MAD: 8.3
3. Forecast Demand for Period 11: 124.5
4. Error for Period 11: Cannot be computed without actual demand for period 11.

Would you like more details on any of these steps or have any other questions?

Relative Questions:

1. How would the forecast change if a different period length for the moving average was used?
2. What is the impact of outliers on the MAD calculation?
3. How does the moving average model compare to other forecasting models, such as exponential smoothing?
4. What is the significance of the MAD in assessing forecast accuracy?
5. How could you use this forecast to make business decisions?
6. What other metrics could be used to assess the accuracy of forecasts?
7. Can you explain the concept of weighted moving averages and how they might be applied here?
8. How might seasonality affect the accuracy of a simple moving average model?

Tip: When using moving averages, the choice of period length can significantly affect the forecast's responsiveness to changes in the data.