ARIMA / SARIMA
Automatic ARIMA or SARIMA forecast with a 95% interval on a single series.
When to use it
Use ARIMA when you have one numeric series and you want a short forecast with a 95% interval. Monthly sales for the next year is the usual case. A series that is stacked across many products is the wrong shape; filter to one series first. A Holt–Winters forecast of the same series is exponential smoothing. Order clues before the fit are autocorrelation.
Assumptions
The target is numeric, with at least eight non-missing values and non-zero variance. An optional date column sorts the rows. Tensr chooses d from a KPSS test (ADF is reported) and D from seasonal strength, then searches p, q, P, and Q by AICc among models that share those differencing orders. It reports both AIC and AICc. Near-unit AR/MA roots are rejected. The search caps the number of parameters relative to the series length after differencing, and it skips seasonal terms when there are fewer than three full seasons.
If a seasonal period of 2 or more is set and the series is long enough, the search includes a seasonal order. The dialog starts that field at 12. The HTTP body default is null, which is a non-seasonal search. Chat dispatch that omits the field uses 12.
A dataset of more than 5,000 rows with repeated dates is rejected as a panel.
Running it in Tensr
Options
Prop
Type
Reading the output
Forty-eight months of sales. A mild upward trend and a 12-month wiggle, with noise of about three units. Seasonal period is 12, so the search includes a seasonal order, 12 steps ahead.
| Step | Forecast | Lower 95% | Upper 95% |
|---|---|---|---|
| 1 | 46.7048 | 38.1211 | 55.2885 |
| 2 | 46.9551 | 38.0314 | 55.8788 |
| 3 | 50.0524 | 41.1018 | 59.0030 |
| 4 | 50.7991 | 41.8464 | 59.7519 |
| 5 | 47.1597 | 38.2068 | 56.1126 |
| 6 | 48.6367 | 39.6837 | 57.5896 |
| 7 | 47.8265 | 38.8735 | 56.7794 |
| 8 | 43.2559 | 34.3030 | 52.2089 |
Selected order (1, 0, 0), seasonal order (1, 1, 0, 12), AIC = 217.872, AICc = 218.622, N = 48. d and D are chosen from unit-root tests first; AICc is compared only among models with those orders. The table is the 12-step forecast with a 95% interval from the fitted model. Seasonal period is 12, so this is a SARIMA search.
Reporting (APA 7)
An automatic SARIMA(1, 0, 0), seasonal order (1, 1, 0, 12) forecast of monthly sales, N = 48, AIC = 217.872, AICc = 218.622. Report the selected order and the forecast interval, not a p-value.
Coming from SPSS
SPSS is Analyze → Forecasting → Create Models with the ARIMA method, or Expert Modeler. Tensr’s item is on the Time series menu, Forecasting → ARIMA / SARIMA. The path string stored for this item matches that menu.
SPSS Expert Modeler searches a wider order space and can keep outliers. Tensr fixes d from KPSS and D from seasonal strength, then searches p, q, P, and Q by AICc on a small grid (p and q up to 2, d up to 1; seasonal P, D, Q on the same bounds). A seasonal period of 12 rebuilds that seasonal grid for every non-seasonal (p, q). This example sets period 12.
Related
Exponential smoothing is the other forecast. STL splits trend from season. Stationarity tests and autocorrelation are the diagnostics.