The partial autocorrelation function (PACF) is primarily used to distinguish between AR (autoregressive) and ARMA (autoregressive moving average) processes.

Key points:

1. For pure AR(p) processes, the PACF cuts off after p lags (becomes zero after lag p).
2. For ARMA processes, the PACF declines gradually in a geometric or exponential pattern rather than cutting off abruptly.
3. This distinction helps in model identification when analyzing time series data.

The text explicitly states: "The most important use of the partial autocorrelation function is in differentiating between AR and ARMA processes."