Autoregressive model
Main article: Autoregressive model
The notation AR(p) refers to the autoregressive model of order p. The AR(p) model is written
X_t = c + \sum_{i=1}^p \varphi_i X_{t-i}+ \varepsilon_t .\,
where \varphi_1, \ldots, \varphi_p are the parameters of the model, c is a constant and \varepsilon_t is white noise. The constant term is omitted by many authors for simplicity.
An autoregressive model is essentially an all-pole infinite impulse response filter with some additional interpretation placed on it.
Some constraints are necessary on the values of the parameters of this model in order that the model remains stationary. For example, processes in the AR(1) model with |φ1| ≥ 1 are not stationary.
X(t)=c+phi_1 X(t-1)+epsilon_t