Discrete Stochastic Processes and Optimal Filtering

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 ...