To calculate the forecast for the 3rd week using Simple Exponential Smoothing (SES) with a smoothing constant (α) of 0.3, we can follow the formula:
\[ F_t = \alpha \cdot x_{t-1} + (1 - \alpha) \cdot F_{t-1} \]
Where:
- \( F_t \) is the forecast for the current week.
- \( x_{t-1} \) is the actual value from the previous week.
- \( F_{t-1} \) is the forecast for the previous week.
We need to start by creating the forecasts for the weeks based on the given data.
-
Initial Forecast (Week 1): For the first forecast \( F_1 \), which we can set as the value for Week 1 (11 in this case), or we can use some other strategy (like the average of the first few data points). Here, we'll keep it simple and assume: \[ F_1 = x_1 = 11 \]
-
Forecast for Week 2: \[ F_2 = \alpha \cdot x_1 + (1 - \alpha) \cdot F_1 \] \[ F_2 = 0.3 \cdot 11 + 0.7 \cdot 11 \] \[ F_2 = 3.3 + 7.7 = 11 \]
-
Forecast for Week 3: \[ F_3 = \alpha \cdot x_2 + (1 - \alpha) \cdot F_2 \] \[ F_3 = 0.3 \cdot 21 + 0.7 \cdot 11 \] \[ F_3 = 6.3 + 7.7 = 14 \]
-
Forecast for Week 4: \[ F_4 = \alpha \cdot x_3 + (1 - \alpha) \cdot F_3 \] \[ F_4 = 0.3 \cdot 7 + 0.7 \cdot 14 \] \[ F_4 = 2.1 + 9.8 = 11.9 \]
Now, let's calculate the forecast for Week 5 using the actual value from Week 4 for calculation:
- Forecast for Week 5 (which is actually forecast for week 3 as per your request): \[ F_5 = \alpha \cdot x_4 + (1 - \alpha) \cdot F_4 \] \[ F_5 = 0.3 \cdot 25 + 0.7 \cdot 11.9 \] \[ F_5 = 7.5 + 8.33 = 15.83 \]
Thus, the forecast for the 3rd week, based on this calculation, is 14.