Machine Learning

2.4.4 Autoregressive Models

We have just seen an example of a stochastic process, namely white noise. We now turn our attention to generating WSS processes via appropriate modeling. In this way, we will introduce controlled correlation among the variables, corresponding to the various time instants. We focus on the real data case, to simplify the discussion.

Autoregressive processes are among the most popular and widely used models. An autoregressive process of order l, denoted as AR(l), is defined via the following difference equation,

$\begin{array}{|l|}\hline \hfill {\text{u}}_n+a_1{\text{u}}_{n-1}+\cdots +a_l{\text{u}}_{n-l}={\mathrm{\eta }}_n:\text{Autoregressive Process},\\ \hline\end{array}$

  (2.138)

where η_n is a white noise process with variance ...