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

112

5

143

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.)**




To calculate the six-period simple moving average (SMA) forecast for each period, you take the average of the demand values from the previous six periods. The forecast can only begin after the first six periods of data are available.

Here are the steps for calculating the six-period SMA for each period from the 7th onward:

### Data Provided:

| Period | Demand |
|--------|--------|
| 1      | 130    |
| 2      | 122    |
| 3      | 121    |
| 4      | 112    |
| 5      | 143    |
| 6      | 105    |
| 7      | 116    |
| 8      | 118    |
| 9      | 142    |
| 10     | 125    |

### Steps:

1. **Calculate the six-period SMA for Period 7:**
   \[
   \text{SMA for Period 7} = \frac{130 + 122 + 121 + 112 + 143 + 105}{6} = \frac{733}{6} \approx 122.2
   \]

2. **Calculate the six-period SMA for Period 8:**
   \[
   \text{SMA for Period 8} = \frac{122 + 121 + 112 + 143 + 105 + 116}{6} = \frac{719}{6} \approx 119.8
   \]

3. **Calculate the six-period SMA for Period 9:**
   \[
   \text{SMA for Period 9} = \frac{121 + 112 + 143 + 105 + 116 + 118}{6} = \frac{715}{6} \approx 119.2
   \]

4. **Calculate the six-period SMA for Period 10:**
   \[
   \text{SMA for Period 10} = \frac{112 + 143 + 105 + 116 + 118 + 142}{6} = \frac{736}{6} \approx 122.7
   \]

### Summary of Six-Period SMA Forecasts:

| Period | SMA Forecast |
|--------|--------------|
| 7      | 122.2        |
| 8      | 119.8        |
| 9      | 119.2        |
| 10     | 122.7        |

These are the six-period simple moving average forecasts for periods 7 through 10.

Would you like any further explanation or help with additional calculations?

---

### Follow-up Questions:

1. What is the formula for a simple moving average with a different period length?
2. How would you compute a weighted moving average?
3. Can you explain the significance of moving averages in forecasting?
4. What is the impact of using a longer period for the moving average on the forecast accuracy?
5. How does the simple moving average compare to exponential smoothing?
6. What are the advantages of using a simple moving average for forecasting?
7. How could you apply a moving average to seasonal data?
8. What happens if there is a significant outlier in the data when using a moving average?

---

**Tip:** The simple moving average smooths out short-term fluctuations and highlights longer-term trends, but it can lag behind sudden changes in the data.

Learn how to compute forecasts using a six-period simple moving average (SMA) model with step-by-step calculations. This problem covers time series analysis and forecasting techniques applied to real-world demand data.

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