Using simple moving averages and the following time series data, respond to each of the items.
 

Period

Demand

1

130

2

122

3

121

4

116

5

141

6

105

7

116

8

118

9

142

10

125




  Click here for the Excel Data File
 
**b.** Compute all possible forecasts using a six-period simple moving average model. **(Round your answers to 1 decimal place.)**



**c.** Compute the MAD. **(Round your answer to 1 decimal place.)**



**d.** What is the forecast demand for period 11? **(Round your answer to 1 decimal place.)**



**e.** What is the error associated with the eleventh-period forecast? **(Round your answer to 1 decimal place.)**






To solve this problem, we'll follow the steps outlined below:

### b. Compute all possible forecasts using a six-period simple moving average model.
A six-period simple moving average forecast is calculated by averaging the demand of the last six periods.

For period 7:
\[
\text{Forecast for Period 7} = \frac{\text{Demand (Period 1 to 6)}}{6} = \frac{130 + 122 + 121 + 116 + 141 + 105}{6} = \frac{735}{6} = 122.5
\]

For period 8:
\[
\text{Forecast for Period 8} = \frac{\text{Demand (Period 2 to 7)}}{6} = \frac{122 + 121 + 116 + 141 + 105 + 116}{6} = \frac{721}{6} = 120.2
\]

For period 9:
\[
\text{Forecast for Period 9} = \frac{\text{Demand (Period 3 to 8)}}{6} = \frac{121 + 116 + 141 + 105 + 116 + 118}{6} = \frac{717}{6} = 119.5
\]

For period 10:
\[
\text{Forecast for Period 10} = \frac{\text{Demand (Period 4 to 9)}}{6} = \frac{116 + 141 + 105 + 116 + 118 + 142}{6} = \frac{738}{6} = 123.0
\]

### c. Compute the MAD (Mean Absolute Deviation).

First, let's calculate the forecast errors (actual demand minus forecast) and their absolute values for periods 7 to 10:

\[
\text{Error for Period 7} = 116 - 122.5 = -6.5, \quad |\text{Error for Period 7}| = 6.5
\]
\[
\text{Error for Period 8} = 118 - 120.2 = -2.2, \quad |\text{Error for Period 8}| = 2.2
\]
\[
\text{Error for Period 9} = 142 - 119.5 = 22.5, \quad |\text{Error for Period 9}| = 22.5
\]
\[
\text{Error for Period 10} = 125 - 123.0 = 2.0, \quad |\text{Error for Period 10}| = 2.0
\]

Now, calculate the MAD:
\[
\text{MAD} = \frac{|\text{Error for Period 7}| + |\text{Error for Period 8}| + |\text{Error for Period 9}| + |\text{Error for Period 10}|}{4} = \frac{6.5 + 2.2 + 22.5 + 2.0}{4} = \frac{33.2}{4} = 8.3
\]

### d. Forecast demand for period 11.
The forecast for period 11 is based on the most recent six periods (Periods 5 to 10):

\[
\text{Forecast for Period 11} = \frac{\text{Demand (Period 5 to 10)}}{6} = \frac{141 + 105 + 116 + 118 + 142 + 125}{6} = \frac{747}{6} = 124.5
\]

### e. Error associated with the eleventh-period forecast.
Since we don't have the actual demand for period 11, we can't calculate the error for period 11. The error can only be determined after the actual demand is known.

### Summary of Answers:
- **b.** 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
- **c.** MAD: 8.3
- **d.** Forecast demand for period 11: 124.5
- **e.** Error for period 11 cannot be determined without the actual demand.

Would you like to go over any details, or do you have further questions?

### Here are 8 follow-up questions you might consider:
1. How would the forecast change if we used a three-period moving average instead?
2. What is the impact of increasing the period in the moving average model on the forecast?
3. How is MAD different from other error measures like MSE (Mean Squared Error)?
4. Can you calculate the standard deviation of the errors for this forecast?
5. How would the forecast for period 11 change if the demand in period 10 was 130 instead of 125?
6. What other smoothing techniques could be used for this data besides a simple moving average?
7. How would you compute a weighted moving average for this data, and what weights might be appropriate?
8. How would the moving average forecast perform if the demand data had a clear trend or seasonality?

### Tip:
Always consider plotting your time series data along with your moving average to visually assess the forecast accuracy and identify any patterns or trends.

Learn how to compute forecasts using a six-period simple moving average model for time series data. Includes step-by-step calculations and Mean Absolute Deviation (MAD) computation. Suitable for advanced high school students.

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