Detrending

How it works

Monthly sales mix three things: the trend (the store growing or shrinking), the season and one-off noise. In a store that grows through the year, the later months look strong because the store is bigger. The growth then reads as a seasonal peak. Detrending estimates the trend and takes it out.

The classical way divides each month by a centred 12-month moving average. Its window spans a full year, so the season averages out and the trend remains. Averaged for each calendar month across years, these ratios give the seasonal indices. The window needs 13 consecutive months for its first value. A store with one year of data can only fit a constant growth rate and divide by that, which gives a rougher estimate. How to measure your own season this way: how seasonal is your store.

Formula

Detrended month = sales in the month ÷ trend value for the same month

Example

Example store, not client data.

The tableware shop grew through the year. Its centred 12-month average is 150,000 in March and 210,000 in November. March brought 135,000, November 315,000. Before detrending, November is 315,000 ÷ 135,000 = 2.33× March. Detrended, March is 135,000 ÷ 150,000 = 0.9 and November is 315,000 ÷ 210,000 = 1.5, so the season alone makes November 1.5 ÷ 0.9 = 1.67× March. The remaining 210,000 ÷ 150,000 = 1.4× is growth.

Not to be confused with

• Year over year — compares a month with the same month a year earlier. The season cancels out and the growth remains, the reverse of detrending.

Right and wrong readings

• Wrong: “Detrending and seasonal adjustment are the same thing.” Right: they remove opposite parts. Detrending takes out the trend to show the season; seasonal adjustment takes out the season to show the trend.
• Wrong: “November is 2.33× March, so that is the size of our peak.” Right: in the example, 1.4× of it is a year of growth. If the growth stops, next November stands at about 1.67× March, not 2.33×.

Sources

• 3.4 Classical decomposition — Hyndman and Athanasopoulos, Forecasting: Principles and Practice (3rd ed.): the 2×12 moving average and the detrended series. Checked 2 October 2026.
• 3.3 Moving averages — the same book: the centred 2×12 moving average weighs 13 months and averages the season out. Checked 2 October 2026.
• 3.2 Time series components — the same book: trend, season, remainder and seasonally adjusted data. Checked 2 October 2026.