Below are the first two values of a time series and the first two values of the exponential smoothing forecast. $$\begin{array}{l}

\begin{array} { l l l }
&&\text { Exp onential Smoothing }\
\text { Time Period } ( t ) & \text { Time Series Value } \left( Y _ { \mathbf { t } } \right) & \text { Forecast } \left( F _ { \mathbf { t } } \right) \
1 & 18 & 18 \
2 & 22 & 18
\end{array}
\end{array}$$ If the smoothing constant equals .3, then the exponential smoothing forecast for time period 3 is _____.
A) 18
B) 19.2
C) 20
D) 40

Question

Below are the first two values of a time series and the first two values of the exponential smoothing forecast. $$\begin{array}{l}

\begin{array} { l l l } 
&&\text { Exp onential Smoothing }\
\text { Time Period } ( t ) & \text { Time Series Value } \left( Y _ { \mathbf { t } } \right) & \text { Forecast } \left( F _ { \mathbf { t } } \right) \
1 & 18 & 18 \
2 & 22 & 18
\end{array}
\end{array}$$ If the smoothing constant equals .3, then the exponential smoothing forecast for time period 3 is _____.
A) 18
B) 19.2
C) 20
D) 40

Quizplus · Accepted Answer

Using the exponential smoothing method with a smoothing constant of 0.3, we can calculate the forecast for time period 3 using the formula:

$F_{3} = \alpha Y_{2} + (1-\alpha) F_{2}$

where $\alpha$ is the smoothing constant, $Y_{2}$ is the time series value at period 2, and $F_{2}$ is the forecast for period 2.

Plugging in the given values, we get:

$F_{3} = 0.3(22) + (1-0.3)(18) = 19.2$

Therefore, the answer is B, $19.2$.

Below Are the First Two Values of a Time Series