To calculate the SES (Simple Exponential Smoothing) forecast for the 3rd week using the given parameters, we can apply the formula for the SES forecast:
\[ F_t = \alpha \cdot X_{t-1} + (1 - \alpha) \cdot F_{t-1} \]
where:
- \( F_t \) is the forecast for the current period
- \( X_{t-1} \) is the actual value of the previous period
- \( F_{t-1} \) is the forecast from the previous period
- \( \alpha \) is the smoothing constant (in this case, \( \alpha = 0.3 \))
Since we do not have an initial forecast \( F_1 \), we can use the actual value of the first week as our starting point for the forecast:
-
Calculate \( F_1 \):
- Assume \( F_1 = X_1 = 5.00 \)
-
Calculate \( F_2 \):
- Actual value for week 1: \( X_1 = 5.00 \)
- Using the formula: \[ F_2 = \alpha \cdot X_1 + (1 - \alpha) \cdot F_1 \] \[ F_2 = 0.3 \cdot 5.00 + 0.7 \cdot 5.00 = 1.5 + 3.5 = 5.00 \]
-
Calculate \( F_3 \):
- Actual value for week 2: \( X_2 = 25.00 \)
- Using the formula: \[ F_3 = \alpha \cdot X_2 + (1 - \alpha) \cdot F_2 \] \[ F_3 = 0.3 \cdot 25.00 + 0.7 \cdot 5.00 = 7.5 + 3.5 = 11.0 \]
-
Calculate \( F_4 \):
- Actual value for week 3: \( X_3 = 22.00 \)
- Using the formula: \[ F_4 = \alpha \cdot X_3 + (1 - \alpha) \cdot F_3 \] \[ F_4 = 0.3 \cdot 22.00 + 0.7 \cdot 11.0 = 6.6 + 7.7 = 14.3 \]
Thus, the forecast for the 3rd week \( F_4 \) is 14.3.
The forecast for the 3rd week is: 14.3.