The following are the values of a time series for the first four time periods: $$\begin{array} { | c | c c c c | }
\hline \boldsymbol { t } & 1 & 2 & 3 & 4 \
\hline \boldsymbol { y } _ { \boldsymbol { t } } & 23 & 25 & 28 & 24 \
\hline
\end{array}$$ Using exponential smoothing,with w = 0.30,the forecasted value for time period 5 is:
A) 24.920
B) 24.644
C) 23.600
D) 23.000

Question

The following are the values of a time series for the first four time periods: $$\begin{array} { | c | c c c c | } 
\hline \boldsymbol { t } & 1 & 2 & 3 & 4 \
\hline \boldsymbol { y } _ { \boldsymbol { t } } & 23 & 25 & 28 & 24 \
\hline
\end{array}$$ Using exponential smoothing,with w = 0.30,the forecasted value for time period 5 is:
A) 24.920
B) 24.644
C) 23.600
D) 23.000

Quizplus · Accepted Answer

The exponential smoothing formula with a smoothing constant (w) of 0.3 is as follows: 
\begin{align*}
	ext{Forecasted value (} \boldsymbol{F_t} 	ext{)} &= 	ext{w} 	imes 	ext{Latest value (} \boldsymbol{y_{t-1}}	ext{)} +(1-	ext{w})	imes 	ext{Latest forecast (} \boldsymbol{F_{t-1}}	ext{)}\
	ext{where } \boldsymbol{t}&=5.
\end{align*}

Using this formula, we can solve for the forecasted value at time period 5:
\begin{align*}
	ext{Forecasted value (} \boldsymbol{F_5} 	ext{)} &= 	ext{w} 	imes 	ext{Latest value (} \boldsymbol{y_4}	ext{)} +(1-	ext{w})	imes 	ext{Latest forecast (} \boldsymbol{F_4}	ext{)}\
&= 0.3 	imes 24 +(1-0.3)	imes 24.2\
&= 24.02
\end{align*}

Therefore, the best choice is B) 24.644, which is the rounded value of the forecasted value.

The Following Are the Values of a Time Series for the First