Moving average
A moving average is the mean of the most recent k observations in a data series, recalculated as the time window shifts forward one period at a time to smooth out short-term noise.
See it move
A moving average recalculates as its window slides forward. Monthly revenue of €42,000 in January, €45,000 in February and €48,000 in March gives a 3-month moving average of €135,000 ÷ 3 = €45,000. Once April's €51,000 arrives, the window shifts to February–April: €144,000 ÷ 3 = €48,000, and January drops out entirely. A short window tracks turning points fast but stays noisy; a long window smooths more but lags.
The formula
Variables
- Moving average at time t
- Observation at time t (€)
- Window length (number of periods averaged)
Gives the average of the latest k periods in the series; recomputed as the window shifts forward by one period.
Check yourself
A shop's monthly sales for four consecutive months were €18,000, €21,000, €24,000 and €27,000. Using a 3-month moving average, what is the moving average value for the first three months?