DEFINITION.– We call the autoregressive process of degree d ∈ any WSS centered X process which verifies :
where B is a white noise of power .
The family of autoregressive processes of degree d is denoted by AR (d).
Thus ∀K, XK is obtained from the d previous values XK−d, …, XK−1 (modulo r.v. BK), which can be carried out using the following schema:
The equality of the definition can be written: H(T) X = B where we have stated that .
This means that we can obtain X by the filtering of B through the filter H(T) whose ...