ARIMA models
Fits an ARIMA(p,d,q)(P,D,Q) model by exact maximum likelihood and forecasts the series with prediction intervals.
Menu: Analyze → Forecasting → ARIMA…
When should I use it?
- Forecasting a series with autocorrelation, trend or seasonality.
- Modelling residual autocorrelation that exponential smoothing does not capture.
What are the assumptions?
- After differencing (d, D) the series is stationary.
- Residuals behave like white noise (check the Ljung-Box test and residual ACF).
How do I run it in StatLab?
- Tick 'Identification' and look at the ACF/PACF of the (differenced) series: a PACF cut-off suggests AR order p, an ACF cut-off suggests MA order q.
- Enter p, d, q (and P, D, Q with the periodicity for seasonal data), choose the constant and the number of forecast periods.
- Check the residual ACF and the Ljung-Box Q(18): a non-significant result means no structure is left.
- Add independent variables (predictors) with optional delays; they need values in the forecast period (leave the series blank there).
- Tick 'Detect outliers' to find additive outliers and level shifts automatically.
How do I read the output?
| Output | Meaning |
|---|---|
| ARIMA Model Parameters | Estimates with SE, t and Sig.; MA terms use the Box-Jenkins sign (1 − θB). |
| Model Fit | Stationary R², RMSE, MAPE, normalized BIC — compare candidate models with BIC (lower is better). |
| Ljung-Box Q(18) | Test for remaining autocorrelation in the residuals. |
| Forecast / UCL / LCL | Point forecasts with prediction limits that widen with the horizon. |
| Numerator, Lag 0 | Effect of a predictor on the series (regression with ARIMA errors). |
| Outliers | Case, type (additive = one-off spike, level shift = permanent step), estimate and t. |
Worked example
On the practice survey dataset (File → Sample dataset), this command — which the dialog's Paste button also produces — runs the procedure:
PROC tsArima /v=score /p=1 /d=0 /q=0 /P=0 /D=0 /Q=0 /s=12 /constant=YES /forecast=12 /conf=95 /preds=(age pre) /outliers=NO /crit=3.5 /ident=NO /racf=NO /save=NO.
Output tables: Model Description · Model Fit statistics · Model Statistics · ARIMA Model Parameters.
How would I report it in APA style?
An ARIMA(1,0,0) model with constant was fitted by exact maximum likelihood (stationary R² = .26, RMSE = 6.92). AR Lag 1: 0.092, p = .263; Age (years) Numerator, Lag 0: 0.191, p < .001; Pre-test score Numerator, Lag 0: 0.257, p < .001. The Ljung-Box test on the residuals did not indicate remaining autocorrelation, Q(17) = 22.91, p = .152.
Computed by StatLab's validated procedure code when this page was built. The example only illustrates the steps; choose variables that fit your own research question.
What are common mistakes?
- Differencing too much (d = 2 when 1 is enough) — it adds noise.
- Keeping a model whose residuals still fail the Ljung-Box test.