autoregression

The term autoregression describes a regression of the variable against itself.

Model

In ARIMA model, autoregression is a regression model that utilizes the dependent relationship between a current observation and observations over a preivous period. An autoregression is run against a set of lagged values of order $p$.

Let $c$ be a constant, ${\varphi }_1,\dots ,{\varphi }_p$ be lag coefficients and ${ϵ}_t$ be a white noise. The AR model is given by

$y(t)=c+{\varphi }_{1}y(t-1)+\cdots +{\varphi }_{p}y(t-p)+{ϵ}_t.$

The simplest model is the AR(1): $y(t)=c+{\varphi }_{1}y(t-1)+{ϵ}_t.$