How to Interpret ACF and PACF plots for Identifying AR, MA, ARMA, or ARIMA Models

In time series analysis, Autocorrelation Function (ACF) and the partial autocorrelation function (PACF) plots are essential in providing the model’s orders such as p for AR and q for MA to select the best model for forecasting.

The basic guideline for interpreting the ACF and PACF plots are as following:

1. Look for tail off pattern in either ACF or PACF.
2. If tail off at ACF → AR model → Cut off at PACF will provide order p for AR(p).
3. If tail off at PACF → MA model → Cut off at ACF will provide order q for MA(q).
4. Tail of at both ACF and PACF → ARMA model

Here are the basic informations when looking at ACF and PACF plots.

• The two blue dash lines pointed by purple arrows represent the significant threshold levels. Anything that spikes over these two lines reveals the significant correlations.
• When looking at ACF plot, we ignore the long spike at lag 0 (pointed by the blue arrow). For PACF, the line usually starts at 1.
• The lag axes will be different depending on the times series data.

ACF Plot Example