ARIMA

Coming soon

Advanced & specialized

This test is implemented and is currently going through StatMinds’ production verification: every statistic is independently checked against a trusted reference (scipy / R), locked with regression tests, and the screen is exercised across assumption-met/violated and significant/non-significant scenarios before it opens up.

See what’s live now

Univariate time-series modelling: AR(p) captures dependence on lagged values, I(d) handles non-stationarity via differencing, MA(q) captures dependence on lagged residuals.

The engine auto-selects (p, d, q) by AIC/BIC over a grid, validates stationarity (ADF / KPSS), residual independence (Ljung-Box), and reports forecasts with prediction intervals via simulation. SARIMA extends ARIMA with seasonal (P, D, Q, s) terms when the series shows periodicity. Standard workhorse for short-to-medium-horizon forecasting of stationary or trend-/seasonality-removable series.

Worked example

What will next month's sales be, given the trend and seasonality?

36 months of sales were modelled with ARIMA after differencing to remove the trend; the model then forecasts ahead with prediction intervals.

Result

An ARIMA(1,1,1) model forecast next month's sales at 1,175 units, 95% prediction interval [1,103, 1,246].

How you'd report it (APA)

An ARIMA(1,1,1) model forecast next-month sales at 1,175 units, 95% prediction interval [1,103, 1,246].

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Univariate short-horizon forecasting
    A retailer forecasts the next 12 months of unit sales for a product line from 5 years (60 monthly observations) of history.
  • Seasonal demand / weather / demand forecasting (SARIMA)
    Hourly electricity demand exhibits daily (s=24) seasonality and weekly (s=168) seasonality.

When NOT to — use instead

  • Multivariate / multi-series joint modelling
    ARIMA is univariate.
  • Volatility / variance forecasting
    ARIMA models conditional MEAN. → GARCH
  • Sub-50 observation series
    ARIMA estimation needs at least ~50 observations for stable p,q identification. → Linear Regression \u2014 OLS (continuous y + predictors)
  • Strong non-linear dynamics (regime-switching, threshold effects)
    ARIMA is linear by construction; non-linear dynamics need TAR / Markov-switching / state-space models.

Hypotheses

H₀: The series is white noise — no significant AR or MA structure (all AR and MA coefficients are zero).
H₁: At least one AR and/or MA term is significantly different from zero.

Parameter tested: AR and MA coefficients with standard errors, z-statistics, and 95% confidence intervals.

Assumptions (and what to do if they fail)

Series is stationary after differencing (constant mean and variance over time).high

Check: ADF p < 0.05 rejects unit root → stationary.

If violated: Non-stationary series produce spurious AR/MA estimates.

No abrupt structural breaks or regime changes in the series.medium

Check: Visual: no obvious jumps or regime shifts.

If violated: Structural breaks invalidate the stationarity assumption and bias forecasts.

Model residuals are white noise (no remaining autocorrelation).high

Check: Ljung-Box p > 0.05 → residuals are white noise.

If violated: Autocorrelated residuals indicate the model has not captured all temporal structure.

Ready to run a ARIMA on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

Run this test →