Measurement of Trend: The Moving Average Method

Meaning

The moving average method measures trend by replacing each value of the series with the average of itself and a fixed number of neighbouring values, smoothing out short-term (seasonal, cyclical, irregular) fluctuations so the underlying trend becomes visible.

Odd period (e.g., 3-yearly, 5-yearly)

For a $3$-yearly moving average, each trend value is

and it centres automatically on the middle year of each group of three. A $5$-yearly moving average works the same way over five consecutive years.

Even period (e.g., 4-yearly, 6-yearly) — needs centring

When the period is even, a moving total or average of, say, four years falls between two years, not on any single year. A second step — a further $2$-yearly moving average of the moving averages already found — centres each value back onto an actual year:

Short illustration. For five years 2018-2022 with values $12, 15, 14, 18, 20$, the 3-yearly moving averages are:

Merits and limitations

• Merits: simple to calculate, objective (no personal judgement, unlike the freehand graphic method), and automatically eliminates the exact period of any regular cyclical/seasonal swing if the moving-average period matches it. …