ARMA and ARIMA Processes

AR($p$) and MA($q$) models are practical specifications to model time series, but they are hardly applied in isolation. It is more common to use them as building blocks of slightly more complex processes: the ARIMA and the ARMA. In this lesson, we will dive into the characteristics of these processes.

Definition

ARMA and ARIMA processes are almost identical. Whether we use one or the other is a matter of our data’s order of integration. Let’s see why.

ARMA

The acronym ARMA stands for Autoregressive Moving Average. In a way, the acronym delivers exactly what it promises: the ARMA process is just a combination of an AR($p$) and an MA($q$):