ARIMA · Free
ARIMA
Bounded (p,d,q ≤ 2) ARMA after a few differences, picked by AICc.
What it assumes
Linear ARMA after a small number of differences. Bounded (p,d,q≤2) search.
When to use
Short-memory autocorrelation after differencing.
When to avoid
Long seasonality (use SARIMA/HW), or n too small for the grid.
Knobs
AICc-selected (p,d,q) with CSS/grid ARMA coefficients.
How it works
ARIMA models short-memory autocorrelation on a differenced series. WhichForecast does not run a huge Python auto-arima: it searches a small grid (p,d,q ≤ 2), uses a differencing heuristic for d, and picks by AICc. Long seasonal patterns need SARIMA or Holt–Winters. A tiny n cannot support the grid. After the fit, rank is still rolling-origin MASE, not the in-sample AICc.
Sample forecast question
These 12 counts wiggle around a rising level. What one-step and three-step ARIMA forecasts does the bounded (p,d,q ≤ 2) search produce?
Step-by-step on these numbers
| Period | Actual | Fitted |
|---|---|---|
| t=1 | 12 | 12 |
| t=2 | 14 | 12 |
| t=3 | 13 | 13.40 |
| t=4 | 16 | 14.50 |
| t=5 | 15 | 14.50 |
| t=6 | 17 | 17.10 |
| t=7 | 16 | 15.80 |
| t=8 | 19 | 17.50 |
| t=9 | 18 | 17.50 |
| t=10 | 20 | 20.10 |
| t=11 | 19 | 18.80 |
| t=12 | 22 | 20.50 |
| Period | Forecast | 95% interval |
|---|---|---|
| t=13 | 20.50 | 18.93 – 22.07 |
| t=14 | 22.75 | 20.53 – 24.97 |
| t=15 | 21.18 | 18.45 – 23.90 |
Parameters the engine found
p= 2d= 1q= 0P= 0D= 0Q= 0m= 1last= 22aicc= 15.165phi1= -0.300phi2= 0.600
The question
These 12 counts wiggle around a rising level. What one-step and three-step ARIMA forecasts does the bounded (p,d,q ≤ 2) search produce? Sample periods: t=1=12, t=2=14, t=3=13, t=4=16, t=5=15, t=6=17, t=7=16, t=8=19, t=9=18, t=10=20, t=11=19, t=12=22 (counts).
Bounded search
WhichForecast does not run a huge auto-arima. It tries d ∈ {0,1,2} and p,q ≤ 2, fits ARMA coefficients on a coarse grid, and picks by AICc. Rank in Excel is still rolling-origin MASE, not this AICc.
Selected model
ARIMA(2,1,0). Coefficients: φ1 = -0.300, φ2 = 0.600. AICc = 15.17.
Forecast
Iterate the ARMA on the differenced scale, then invert differences. t=13: 20.50; t=14: 22.75; t=15: 21.18.
Interval
Residual σ = 0.802. For h = 1 the 95% band is [18.93, 22.07] around 20.50. The engine labels this a residual-Gaussian heuristic (σ√h), not a simulation interval.
Graph of this sample
The chart plots the canned table on this page (actuals, in-sample fitted, forecast, 95% interval). Not your Excel series. Free analysis never uploads raw data.
Educational only. Not investment, weather, or operational advice. In the add-in, rank is rolling-origin MASE — “best supported among candidates on this series.”