autoregressive model

The autoregressive model of order $p$, denoted AR($p$), is a random process model described by

$$y_t=\sum _{i=1}^p{a}_i{y}_{t-i}+c+e_t,t=1,2,\mathrm{\dots }$$(1)

where $a_i$ are model parameters, $y_t$ is the model output in discrete time instant $t$. Term $c$ is an absolute term (constant) and $e_t$ denotes discrete white noise.

A first-order autoregression model AR(1) in the form $y_t=a{y}_{t-1}+c+e_t$ is one major example.