The following are the values of a time series for the first four time periods: $\begin{array} { | c | c c c c | }
\hline t & 1 & 2 & 3 & 4 \
\hline y _ { t } & 23 & 25 & 28 & 24 \
\hline
\end{array}$ Using exponential smoothing, with w = 0.25, the forecast value for time period 5 is:
A) 18.352.
B) 23.500.
C) 24.469.
D) 23.000.

Question

The following are the values of a time series for the first four time periods: $\begin{array} { | c | c c c c | } 
\hline t & 1 & 2 & 3 & 4 \
\hline y _ { t } & 23 & 25 & 28 & 24 \
\hline
\end{array}$ Using exponential smoothing, with w = 0.25, the forecast value for time period 5 is:
A) 18.352.
B) 23.500.
C) 24.469.
D) 23.000.

Quizplus · Accepted Answer

Using exponential smoothing with weight w=0.25, we have:

F$_{t+1}$ = wY$_t$ + (1-w)F$_t$ for t = 1,2,3, ...

where F$_1$ = Y$_1$.

In this case, we have:

F$_2$ = wY$_1$ + (1-w)F$_1$ = 0.25(23) + 0.75(23) = 23

F$_3$ = wY$_2$ + (1-w)F$_2$ = 0.25(25) + 0.75(23) = 23.5

F$_4$ = wY$_3$ + (1-w)F$_3$ = 0.25(28) + 0.75(23.5) = 24.125

Therefore, the forecast value for time period 5 is:

F$_5$ = wY$_4$ + (1-w)F$_4$ = 0.25(24) + 0.75(24.125) = 24.469

Hence, the best choice is C.

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