The following are the values of a time series for the first four time periods:

t	1	2	3	4
yt	25	27	30	26
Use the simple exponential smoothing technique with α = 0.3, what is the forecast for time period 5?

To forecast the value for time period 5 using the Simple Exponential Smoothing (SES) technique, we follow these steps:

1. **Initialize the forecast**: Start with the initial value \( F_1 \). Often, the first observation is used as the initial forecast, so we set \( F_1 = y_1 = 25 \).

2. **Apply the smoothing formula**: The forecast for the next period is calculated using the formula:
   \[
   F_{t+1} = \alpha y_t + (1 - \alpha) F_t
   \]
   where:
   - \( F_{t+1} \) is the forecast for the next period.
   - \( \alpha \) is the smoothing constant (0.3 in this case).
   - \( y_t \) is the actual value in the current period.
   - \( F_t \) is the forecast for the current period.

Let's calculate the forecast for each period up to period 5.

### Calculation
1. **Period 1**: \( F_1 = y_1 = 25 \) (initial forecast)
2. **Period 2**: \( F_2 = \alpha y_1 + (1 - \alpha) F_1 \)
   \[
   F_2 = 0.3 \cdot 25 + 0.7 \cdot 25 = 25
   \]
3. **Period 3**: \( F_3 = \alpha y_2 + (1 - \alpha) F_2 \)
   \[
   F_3 = 0.3 \cdot 27 + 0.7 \cdot 25
   \]
   \[
   F_3 = 8.1 + 17.5 = 25.6
   \]
4. **Period 4**: \( F_4 = \alpha y_3 + (1 - \alpha) F_3 \)
   \[
   F_4 = 0.3 \cdot 30 + 0.7 \cdot 25.6
   \]
   \[
   F_4 = 9 + 17.92 = 26.92
   \]

5. **Period 5**: \( F_5 = \alpha y_4 + (1 - \alpha) F_4 \)
   \[
   F_5 = 0.3 \cdot 26 + 0.7 \cdot 26.92
   \]
   \[
   F_5 = 7.8 + 18.844 = 26.644
   \]

The forecast for time period 5 is **26.644**.

Would you like more details or have any questions?  
Here are some related questions:

1. How does changing the value of \( \alpha \) affect the forecast?
2. What is the main assumption behind the Simple Exponential Smoothing technique?
3. How can we select an appropriate \( \alpha \) value for SES?
4. Can Simple Exponential Smoothing handle trends in time series data?
5. How does the initial forecast affect the subsequent forecasts in SES?
6. What are the advantages of using Simple Exponential Smoothing?
7. How would you compare SES with moving averages for forecasting?
8. What are the limitations of the Simple Exponential Smoothing technique?

**Tip:** The choice of the smoothing constant \( \alpha \) greatly influences the responsiveness of the forecast. A higher \( \alpha \) gives more weight to recent observations, making the forecast more sensitive to recent changes.

Learn how to forecast time series data using Simple Exponential Smoothing with α = 0.3. This technique involves iterative smoothing of previous forecasts and actual values to predict future trends. Suitable for advanced learners and practitioners.

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