Time series and forecasting · insight-0232
Read ACF and PACF as hints, then choose orders by information criteria and residual checks
- Evidence type
- practitioner heuristic
- Difficulty
- medium
- Roles
- Data scientist
- Industries
- cross-industry
Summary: situation, action, reason, boundary
Situation
An analyst picks ARIMA(2,1,1) because the PACF 'cuts off at lag 2'.
Action
Use the plots to narrow candidates, compare them with AICc on the same differencing, check residuals with a Ljung-Box test, and finally compare forecasts in a backtest against a seasonal naive baseline.
Reason
Residual tests check whether information is left in the residuals, but neither the plots nor the test prove forecast accuracy; only out-of-sample error does.
Boundary
Classical ARIMA work and feature-lag selection for ML forecasts.
Symptom or risk
ACF and PACF patterns of real series are often ambiguous; mixed ARMA processes, trends and seasonality blur the textbook signatures, so orders chosen by eye are arbitrary.
Exceptions
Clean simulated AR or MA processes do show textbook patterns; use them for teaching, not as evidence for real data.
Trade-offs
Automated order search is fast but can overfit with many candidate models.
Pitfalls
Comparing AICc across models with different orders of differencing.
Lessons and concepts
Claims and their sources
The Ljung-Box statistic tests whether a group of residual autocorrelations differs from what white noise would produce.