Stationarity is the property that makes the past a reliable guide to the future in many models.
If the statistical behaviour of a series stays the same, patterns learned from one stretch apply to another.
Most real business series are not stationary, because of trends, seasons and changes in spread.
A series with a rising mean, such as growing sales, is not stationary.
A series whose spread grows over time, such as ever more volatile sales, is not stationary either.
Taking the change from one period to the next removes a steady trend.
Subtracting the value from one season earlier removes a stable seasonal pattern.
Taking logarithms first can steady a spread that grows with the level.
A random walk, where each value is the last plus a random step, is the classic series that is not stationary.
Share prices often behave like random walks, which is why their daily changes are studied instead.
The augmented Dickey-Fuller test checks for a random walk, while the KPSS test checks the opposite claim.
Tests can disagree on short or messy series, so plots of the series and its autocorrelation matter as much.
Transforming a series that is already stationary adds noise and can make forecasts worse.
In practice, analysts transform until the series looks stable, then confirm with a test.
The common misconception is that stationary means constant, when a stationary series can wiggle a lot around a steady level.