8.7 Autoregression - AR - Overview

We forecast using a linear combination of past values of the variable. In other words, it is a linear regression where the predictors are the previous observations

The term autoregression describes a regression of the variable against itself. 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): $y(t)=c+{\varphi }_{1}y(t-1)+{ϵ}_t.$