Since AR(p) and MA(q) terms interact, the information provided by the ACF and PACF is no longer reliable and can only be used as a starting point.

Traditionally, the AIC and BIC information criteria have been used to rely on in-sample fit when selecting the model design. Alternatively, we can rely on out-of-sample tests to cross-validate multiple parameter choices.

The following summary provides some generic guidance to choose the model order in the case of considering AR and MA models in isolation:

• The lag beyond which the PACF cuts off is the indicated number of AR terms. If the PACF of the differenced series cuts off sharply and/or the lag-1 autocorrelation is positive, add one or more AR terms.
• The lag beyond which the ACF cuts off is the indicated number of MA terms. If the ACF of the differenced series displays a sharp cutoff and/or the lag-1 autocorrelation is negative, consider adding an MA term to the model.
• AR and MA terms may cancel out each other's effects, so always try to reduce the number of AR and MA terms by 1 if your model contains both to avoid overfitting, especially if the more complex model requires more than 10 iterations to converge.
• If the AR coefficients sum to nearly 1 and suggest a unit root in the AR part of the model, eliminate 1 AR term and difference the model once (more).
• If the MA coefficients sum to nearly 1 and suggest a unit root in the MA part of the model, eliminate 1 MA term and reduce the order of differencing by 1.
• Unstable long-term forecasts suggest there may be a unit root in the AR or MA part of the model.