Question

Using the date below, what is the simple exponential smoothing forecast for the 4th week where alpha =.3?
Week1, Time series=6
Week2, Time series=4
Week3, Time series=3
Week4, Time series=6

Answer 1

To calculate the simple exponential smoothing forecast for the 4th week using the given values and an alpha (α) of 0.3, we can follow the formula for exponential smoothing:

\[
F_t = \alpha \cdot X_{t-1} + (1 - \alpha) \cdot F_{t-1}
\]

Where:
- \( F_t \) = Forecast for the current period
- \( α \) = Smoothing constant (in this case, 0.3)
- \( X_{t-1} \) = Actual value from the previous period (the time series value)
- \( F_{t-1} \) = Forecast from the previous period

Since we do not have an initial forecast for Week 1, we will assume the first forecast is equal to the first observed value (or you could choose to start with a different value).

Let's denote:
- Forecast for Week 1, \( F_1 = X_1 = 6 \)

Now, we can calculate the forecasts for the subsequent weeks:

### Week 2:
\[
F_2 = \alpha \cdot X_1 + (1 - \alpha) \cdot F_1
\]
\[
F_2 = 0.3 \cdot 6 + 0.7 \cdot 6 = 6
\]

### Week 3:
\[
F_3 = \alpha \cdot X_2 + (1 - \alpha) \cdot F_2
\]
\[
F_3 = 0.3 \cdot 4 + 0.7 \cdot 6
\]
\[
F_3 = 1.2 + 4.2 = 5.4
\]

### Week 4:
\[
F_4 = \alpha \cdot X_3 + (1 - \alpha) \cdot F_3
\]
\[
F_4 = 0.3 \cdot 3 + 0.7 \cdot 5.4
\]
\[
F_4 = 0.9 + 3.78 = 4.68
\]

Thus, the simple exponential smoothing forecast for the 4th week (Week 4) is approximately **4.68**.