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AR model

The autoregressive (AR) model of an order p can be written as AR(p) and is defined as  
X_t = \alpha_1 X_{t-1} + \cdots + \alpha_{t-p} X_{t-p} + Z_t\end{displaymath} (8)
where Zt is a purely random process and $ \text{E} (Z_t) = 0, \textrm{Var} (Z_t) = \sigma_Z^2 $.The parameters $\alpha_1, \ldots, \alpha_p$ are called the AR coefficients.

The name ``autoregressive'' comes from the fact that Xt is regressed on the past values of itself.

Example: AR(1) or Markov process

The series will converge if $\vert\alpha\vert < 1$.From the properties of the random process Zt, we can obtain that