Calculate moving means

Calculating moving means

A moving mean averages a complete consecutive window of observations. An odd-term window is placed at its central period, while an even-term window needs a second averaging step to centre it

1. Use a complete consecutive window For an odd window, place the requested period at the centre of the selected observations \(\displaystyle M_6=\frac{x_4+x_5+x_6+x_7+x_8}{5}\)
2. Divide by the window width The divisor is the number of observations in the selected window, not the full series length \(\displaystyle \frac{120+135+150}{3}=135\)
3. Leave unsupported ends blank A window cannot be centred at an end period unless every required observation is available \(\displaystyle N=8,\ k=3\Rightarrow N-k+1=6\text{ supported means}\)
4. Centre an even window Calculate adjacent preliminary means and average them at the intervening original period \(\displaystyle A_1=16,\ A_2=20,\ C_3=\frac{A_1+A_2}{2}=18\)

Worked example

A community pool records visitor counts of 84, 96, 108, 120 and 132 over five consecutive days. Calculate the 5-term moving mean at Day 3

1. \(\displaystyle 84,\ 96,\ 108,\ 120,\ 132\)These five consecutive observations form the window centred on Day 3
2. \(\displaystyle 84+96+108+120+132=540\)Add the observations in the window to obtain the window sum
3. \(\displaystyle M_3=\frac{540}{5}=108\)Divide the window sum by the five terms to get the moving mean

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