Definition
The notation AR(p) indicates an autoregressive model of order p. The AR(p) model is defined as
where are the parameters of the model, is a constant (often omitted for simplicity) and is white noise.
An autoregressive model can thus be viewed as the output of an all-pole infinite impulse response filter whose input is white noise.
Some constraints are necessary on the values of the parameters of this model in order that the model remains wide-sense stationary. For example, processes in the AR(1) model with |φ1| ≥ 1 are not stationary. More generally, for an AR(p) model to be wide-sense stationary, the roots of the polynomial must lie within the unit circle, i.e., each root must satisfy .
Read more about this topic: Autoregressive Model
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