Question

Week Time series Value
1 17
2 12
3 21
4 19
________________________________________
Using the above data, what is Simple Exponential Smoothing Forecast for 5th week where α=0.3

Answer 1

To calculate the Simple Exponential Smoothing Forecast for the 5th week using a smoothing constant \(\alpha = 0.3\), we'll first need to establish the formula:

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

Where:
- \(F_t\) is the forecast for the current time period.
- \(Y_{t-1}\) is the actual value from the previous time period.
- \(F_{t-1}\) is the forecast from the previous time period.

We need an initial forecast, often taken to be the first actual value. In this case, we can take:

\[
F_1 = Y_1 = 17
\]

Now, we will proceed to calculate the forecasts for the subsequent weeks.

### Week 2:
\[
F_2 = \alpha \cdot Y_1 + (1 - \alpha) \cdot F_1
\]
\[
F_2 = 0.3 \cdot 17 + 0.7 \cdot 17 = 17
\]

### Week 3:
\[
F_3 = \alpha \cdot Y_2 + (1 - \alpha) \cdot F_2
\]
\[
F_3 = 0.3 \cdot 12 + 0.7 \cdot 17 = 3.6 + 11.9 = 15.5
\]

### Week 4:
\[
F_4 = \alpha \cdot Y_3 + (1 - \alpha) \cdot F_3
\]
\[
F_4 = 0.3 \cdot 21 + 0.7 \cdot 15.5 = 6.3 + 10.85 = 17.15
\]

### Week 5:
Now, we can calculate the forecast for the 5th week using the actual value from the 4th week and the forecast from the 4th week.

\[
F_5 = \alpha \cdot Y_4 + (1 - \alpha) \cdot F_4
\]
\[
F_5 = 0.3 \cdot 19 + 0.7 \cdot 17.15 = 5.7 + 12.005 = 17.705
\]

Thus, the Simple Exponential Smoothing Forecast for the 5th week is approximately **17.71**.