ARIMA Order Selection Calculator

Work out arima order selection instantly with clear inputs, formula shown and shareable results.

About ARIMA Order Selection Calculator

The classical Box-Jenkins reading is that the PACF cut-off suggests the AR order p and the ACF cut-off suggests the MA order q, with d set by how many differences the series needs to become stationary. Parameter count then dictates how much history you need: roughly ten observations per parameter, and at least two or three full seasonal cycles when a seasonal term is included.

Formula

Order identification

p = last significant PACF lag; q = last significant ACF lag; d = differences for stationarity; parameters ~ p + q + seasonal terms + constant

Worked example

With the default values below, ARIMA Order Selection Calculator returns Suggested non-seasonal order of ARIMA(1,1,2). Change any input above and every figure here is recalculated in your browser.

Inputs used

Differences needed for stationarity (d)accepts 0–3: 1
Significant ACF lagsaccepts 0–30: 2
Significant PACF lagsaccepts 0–30: 1
Seasonal period (m)minimum 1: 12

Results

Suggested non-seasonal order: ARIMA(1,1,2)
Suggested seasonal order: Seasonal (1,1,1)[12]
Parameters to estimate: 6
Minimum observations recommended: 60

Step by step

1Values used
2Order identification
3Suggested non-seasonal order= ARIMA(1,1,2)
4Suggested seasonal order= Seasonal (1,1,1)[12]
5Parameters to estimate= 6
6Minimum observations recommended= 60

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Should I just use auto ARIMA?

Automatic order selection by AICc is a strong default and usually beats manual reading. Use ACF and PACF plots to sanity-check its answer rather than to replace it.

How do I know d?

Apply a unit-root test such as KPSS and difference until it passes. Over-differencing shows up as a large negative spike at lag 1 in the ACF and inflates forecast variance.