Auto ARIMA Selector Calculator

1. Paste your series as values, or as two columns (label/date and value).
2. Choose AIC for quicker selection, or BIC for stricter simplicity.
3. Set differencing d for trend; enable seasonality and set m if needed.
4. Start with small bounds (e.g., max p,q = 3, seasonal P,Q = 1).
5. Press Submit. Results appear above the form with downloads and charts.

Why automated order selection matters

Auto ARIMA screens many ARIMA(p,d,q) and seasonal (P,D,Q)[m] options to reduce manual trial. With max p,q at 3 and seasonal P,Q at 1, the search evaluates up to 64 candidates. A smaller grid often beats one complex model because it limits overfitting on short series and stays interpretable for most teams.

Inputs that shape the search space

Differencing settings control stationarity. A common starting point is d=1 for trending monthly data and D=1 when a 12‑month pattern persists after detrending. Keep m smaller than the sample length; with 36 points, m=12 leaves only 24 seasonally differenced values. Forecast horizon h should match decisions; for inventory, 4–12 steps is typical, while budgeting may need 12–24. Compute budget caps runtime; 800–1500 ms is typical.

How scoring balances fit and complexity

This calculator ranks models using AIC or BIC. Both use the conditional log‑likelihood ℓ and parameter count k. AIC = 2k − 2ℓ favors predictive accuracy, while BIC = k·ln(n) − 2ℓ adds a stronger penalty as effective observations n grow. When n is near 30, BIC’s penalty is roughly 3.4k; at n=120 it is about 4.8k. If AIC and BIC disagree, prefer BIC for sparse data.

Reading diagnostics before deployment

After selection, check residual mean and standard deviation; a mean near zero indicates unbiased errors. The ACF lags 1–10 help detect leftover structure: values within ±0.2 are often acceptable for quick screening, and a slow decay can suggest under-differencing. If early lags stay high, raise d, enable seasonality, or allow p to increase. Also compare sigma² across top candidates; large jumps can flag unstable fits.

Practical workflow for model iteration

Start with conservative bounds, run selection, then refine around the top candidates by narrowing p and q to top values. If the best model has p=0 and q=0, try disabling the intercept to test a simpler baseline. For seasonality, confirm that m matches the real cycle (7 for daily‑weekly, 12 for monthly, 24 for hourly‑daily). Finally, backtest with a holdout window of 10–20% of observations, comparing MAE or MAPE alongside the chosen criterion, and keep the model that remains stable across at least two adjacent windows.

Which data formats are supported?

Paste one number per line, space‑separated values, or two columns like Date,Value. Headers are ignored. The selector extracts numeric values and uses their order as the time index.

How do I choose AIC vs BIC?

Use AIC when forecasting accuracy is the priority and you have enough data. Use BIC when you want a simpler model, especially with shorter series, because it penalizes extra parameters more strongly.

What do d and D control?

d applies regular differencing to remove trend. D applies seasonal differencing at period m to remove repeating cycles. Start with d=1 for trend and D=1 only if the seasonal pattern remains after detrending.

When should I enable seasonal terms?

Enable seasonality when your series repeats with a stable period, such as weekly demand (m=7) or monthly metrics (m=12). If you are unsure, run once without seasonality and compare top candidate scores.

Why did the search stop before checking all models?

The compute budget limits runtime. When the elapsed time exceeds the budget, the tool returns the best model found so far. Reduce max orders or increase the budget if you need a wider search.

How should I validate the selected model?

Hold out the last 10–20% of observations, refit on the earlier portion, and compare errors like MAE or MAPE. Check residual ACF for remaining structure, then confirm stability by shifting the holdout window.