To compute the six-period simple moving average (SMA) for the given time series data, we'll calculate the average of the demand for each set of six consecutive periods. The formula for the six-period SMA at period $t$ is:

$\text{SMA}_t = \frac{D_{t-1} + D_{t-2} + D_{t-3} + D_{t-4} + D_{t-5} + D_{t-6}}{6}$

Where $D_t$ represents the demand at period $t$.

Given the dataTo compute the six-period simple moving average (SMA) for the given time series data, we'll calculate the average of the demand for each set of six consecutive periods. The formula for the six-period SMA at period $t$ is:

$\text{SMA}_t = \frac{D_{t-1} + D_{t-2} + D_{t-3} + D_{t-4} + D_{t-5} + D_{t-6}}{6}$

Where $D_t$ represents the demand at period $t$.

Given the

\hline \text{Period} & \text{Demand} \\ \hline 1 & 130 \\ 2 & 122 \\ 3 & 121 \\ 4 & 112 \\ 5 & 143 \\ 6 & 105 \\ 7 & 116 \\ 8 & 118 \\ 9 & 142 \\ 10 & 125 \\ \hline \end{array}$$ The forecasts start from period 7 because the first six periods are needed to compute the first six-period SMA. ### Step-by-Step Calculations: 1. **Period 7:** $$\text{SMA}_7 = \frac{130 + 122 + 121 + 112 + 143 + 105}{6} = \frac{733}{6} = 122.2$$ 2. **Period 8:** $$\text{SMA}_8 = \frac{122 + 121 + 112 + 143 + 105 + 116}{6} = \frac{719}{6} = 119.8$$ 3. **Period 9:** $$\text{SMA}_9 = \frac{121 + 112 + 143 + 105 + 116 + 118}{6} = \frac{715}{6} = 119.2$$ 4. **Period 10:** $$\text{SMA}_{10} = \frac{112 + 143 + 105 + 116 + 118 + 142}{6} = \frac{736}{6} = 122.7$$ ### Final Forecasts: $$\begin{array}{|c|c|} \hline \text{Period} & \text{Forecast (SMA)} \\ \hline 7 & 122.2 \\ 8 & 119.8 \\ 9 & 119.2 \\ 10 & 122.7 \\ \hline \end{array}$$ These forecasts represent the predicted demand for periods 7 through 10 using the six-period simple moving average. --- Would you like any further details or have any questions? Here are some follow-up questions you might find interesting: 1. What are the advantages and disadvantages of using a simple moving average? 2. How does the length of the moving average period affect the forecast? 3. What other smoothing techniques could be applied to this data? 4. How would the forecast change if we used a three-period moving average? 5. Can we improve the accuracy of the forecast by weighting the periods differently? 6. How would you calculate the mean absolute error (MAE) for these forecasts? 7. What might cause the forecast to differ significantly from the actual demand? 8. How does this method compare to exponential smoothing? **Tip:** When working with time series data, it's important to choose a moving average period that balances the need for smoothing out noise with the requirement to respond to recent changes in the data.