ARMA is an acronym for auto regressive moving average; a stochastic process modelling time series. It adds moving average terms to the AR model.
Overview
ARMA is an acronym for auto regressive moving average; a stochastic process modelling time series. It adds moving average terms to the AR model. Mathematically, a moving average model is specified by its order $q$. An order $q$ moving average model, MA(q) for a time series $Y_t$ is written as follows:
$$Y_t = \epsilon_t + \sum_{i=1}^q \theta_i \epsilon_{t-i}$$
Here $\epsilon_{t-i}$ ($i=0,1,2,\ldots q$) represent white noise, and $\theta_i$ ($i=1,2,\ldots q$) represent the parameters of the model.
An ARMA model is the combination of an AR(p) and MA(q) model. It is represented as ARMA(p,q), and takes the following mathematical form:
$$Y_t = c + \epsilon_t + \sum_{i=1}^p \phi_i Y_{t-i} + \sum_{i=1}^q \theta_i \epsilon_{t-i}$$
ARMA models are a special case of ARIMA models.
