Given the following time series data: $12$, $15$, $14$, $16$, $18$, and using the simple exponential smoothing (SES) method with smoothing constant $\alpha =0.3$, what is the forecast for the next period (period $6$) if the initial forecast for period $1$ is $12$?

• A. $15.17$
• B. $15.10$
• C. $15.29$
• D. $16.00$

Answer: (C)

Verified step by step guidance

1. Identify the given data points: the observed values for periods 1 to 5 are 12, 15, 14, 16, and 18 respectively. The smoothing constant \( \alpha = 0.3 \), and the initial forecast for period 1 is given as 12.
2. Recall the formula for Simple Exponential Smoothing (SES) forecast: \[ F_{t+1} = \alpha \times A_t + (1 - \alpha) \times F_t \] where \( F_{t+1} \) is the forecast for the next period, \( A_t \) is the actual value at time \( t \), and \( F_t \) is the forecast for time \( t \).
3. Start with the initial forecast \( F_1 = 12 \). Use the actual value for period 1 (which is 12) to calculate the forecast for period 2 using the SES formula.
4. Iteratively apply the SES formula for each subsequent period: use the actual value \( A_t \) and the forecast \( F_t \) from the previous step to find \( F_{t+1} \) for periods 3, 4, 5, and finally 6.
5. After calculating \( F_6 \), this value will be the forecast for period 6. This completes the process of forecasting using simple exponential smoothing with the given data and smoothing constant.