Autoregressive processes arise frequently in econometrics. For example, we might have a simple dynamic model of the form:
yt = β0 + β1yt-1 + εt ; εt ~ i.i.d.[0 , σ2] . (1)
Or, we might have a regression model in which everything is "standard", except that the errors follow an autoregressive process:
yt = β0 + β1xt + ut (2)
ut = ρ ut-1 + εt ; εt ~ i.i.d.[0 , σ2] .
In each of these examples a first-order autoregressive, or AR(1), process is involved.
Higher-order AR processes are also commonly used. Although most undergrad. econometrics students are familiar with the notion of "stationarity" in the context of an AR(1) process, often they're not aware of the conditions needed to ensure the stationarity of more general AR models. Let's take a look at this issue.