Suppose that we calculate the four-period moving average of the following time series $$\begin{array} { | c | c c c c | c | c | }
\hline \boldsymbol { t } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \boldsymbol { y } _ { \mathbf { t } } & 16 & 28 & 21 & 15 & 26 & 12 \
\hline
\end{array}$$ The centered moving average for period 3 is:
A) 22.5
B) 21.25
C) 20.50
D) 18.5

Question

Suppose that we calculate the four-period moving average of the following time series $$\begin{array} { | c | c c c c | c | c | } 
\hline \boldsymbol { t } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \boldsymbol { y } _ { \mathbf { t } } & 16 & 28 & 21 & 15 & 26 & 12 \
\hline
\end{array}$$ The centered moving average for period 3 is:
A) 22.5
B) 21.25
C) 20.50
D) 18.5

Quizplus · Accepted Answer

To calculate the centered moving average for period 3, we need to take the average of the second and the third period moving averages.

The four-period moving average is:

\begin{align*}
	ext{Period 4 MA} &= \frac{16+28+21+15}{4} = 20\
	ext{Period 5 MA} &= \frac{28+21+15+26}{4} = 22.5\
	ext{Period 6 MA} &= \frac{21+15+26+12}{4} = 18.5
\end{align*}

So the centered moving average for period 3 is:

$$	ext{Centered MA}_{3} = \frac{	ext{Period 4 MA}+	ext{Period 5 MA}}{2} = \frac{20+22.5}{2} = 21.25 $$

Therefore, the answer is B).

Suppose That We Calculate the Four-Period Moving Average of the Following