Time series and forecasting · insight-1230
Take the seasonal difference first and let a seasonal-strength measure decide whether you need one
- Evidence type
- documented fact
- Difficulty
- easy
- Roles
- Data scientist, Data analyst
- Industries
- aviation, retail, energy
Summary: situation, action, reason, boundary
Situation
Daily bookings show a strong weekly pattern and a trend, and an analyst applies a first difference and then wonders why the weekly spikes are still there.
Action
Measure seasonal strength on an STL decomposition. If it is high, apply one seasonal difference first, then test whether a first difference is still needed, and confirm the ordering against the alternative in a backtest.
Reason
A seasonally differenced series is sometimes already stationary, so doing it first can save a difference. The FPP3 rule suggests one seasonal difference when seasonal strength reaches 0.64 and none below it.
Boundary
ARIMA-family models on series whose seasonal pattern is stable from year to year.
Symptom or risk
A first difference leaves the seasonal pattern in the series, so the model needs extra seasonal terms, or the analyst stacks further differences that are not required.
Exceptions
Seasonality that changes shape over time may be better handled with Fourier terms or STL than with a rigid seasonal difference.
Trade-offs
A seasonal difference consumes one full period of history and adds noise when seasonality is weak.
Pitfalls
Applying both a seasonal and a first difference by habit instead of differencing as little as necessary.
Lessons and concepts
Claims and their sources
FPP3 recommends applying the seasonal difference first because the result may already be stationary, and its seasonal-strength rule suggests no seasonal difference when strength is below 0.64 and one otherwise.