Glossary

Stationarity

The property of a time series whose statistical characteristics, such as mean and variance, stay constant over time.

A time series is stationary when its statistical properties, chiefly its mean, variance, and autocorrelation structure, stay constant over time rather than drifting or trending. A stationary series still fluctuates period to period, but the fluctuations are drawn from the same underlying distribution throughout the series, rather than one that is shifting.

Most series encountered in practice are not stationary in raw form: sales grow with the business, prices trend with inflation, and traffic follows seasonality. Analysts commonly transform a non-stationary series into a stationary one, most often by differencing, subtracting each value from the previous one, before fitting models such as ARIMA that assume stationarity, or "integrated" variants that build differencing into the model itself. This differs from simple trend removal: stationarity requires the variance and the correlation structure to be stable too, not just the level.

Stationarity matters because many classical time-series methods, and the statistical guarantees behind their forecasts and confidence intervals, are only valid when it holds; fitting them to a non-stationary series can produce misleadingly confident time series forecasting. Common diagnostics include visually inspecting the series and checking autocorrelation at increasing lags, alongside formal statistical tests. A related pitfall is a structural break, a sudden shift in the series' behavior that stationarity tests may miss unless paired with change-point detection.

Last reviewed September 22, 2026

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Related terms

Autocorrelation The correlation of a time series with a lagged, delayed copy of itself, used to detect repeating patterns and dependence over time. ARIMA (autoregressive integrated moving average) A classical time-series forecasting model that combines a series' own past values, differencing, and past forecast errors. Time series forecasting Predicting future values of a metric using patterns found in its own historical sequence over time. Seasonality A regular, predictable pattern in data that repeats at a fixed calendar interval, such as daily, weekly, or annually. Change-point detection Identifying the points in a time series where its underlying statistical behavior shifts abruptly rather than drifting gradually.

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