Stationarity And Differencing
A series is stationary when its statistical behavior does not change over time. Many classic forecasting models assume this property.
What stationary means
- The mean stays roughly constant, with no drifting trend.
- The variance stays roughly constant, with no widening swings.
- The autocorrelation depends only on the gap between points, not on where you look.
Why it matters
A trending or seasonal series breaks these rules. Fitting a model to such data can give estimates that change as the series moves, leading to poor forecasts.
Differencing
Differencing replaces each value with the change from the previous value. This removes a trend by focusing on movement instead of level.
- First difference: subtract the prior value to flatten a linear trend.
- Seasonal difference: subtract the value one season ago to remove a repeating cycle.
A statistical check like the augmented Dickey Fuller test helps confirm whether differencing made the series stationary.
Key idea
Stationarity means stable statistics over time, and differencing removes trend so the series settles into a modelable form.