**3.5. Important example: autoregressive process**

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*, *X*_{K} is obtained from the *d* previous values *X*_{K−d}, …, *X*_{K−1} (modulo r.v. *B*_{K}), which can be carried out using the following schema:

**Figure 3.8.** *Autoregressive filter*

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 ...