When is an Autoregressive Model Dynamically Stable?

Autoregressive processes arise frequently in econometrics. For example, we might have a simple dynamic model of the form:

            y_t = β₀ + β₁y_t-1 + ε_t   ;   ε_t ~ 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:

            y_t = β₀ + β₁x_t + u_t               (2)

             u_t = ρ u_t-1 + ε_t    ;  ε_t ~ 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.

Special Issues of "Computational Statistics & Data Analysis"

One of the statistics journals that's always on my watch-list (and for whom I sometimes referee) is Computational Statistics and data Analysis. CSDA regularly publishes issues devoted to special topics, including topics explicitly related to econometrics. Indeed, six special issues on Computational Econometrics have been published to date, including the 1^st issue of the Annals of Computational and Financial Econometrics, released last year.

Recently, the call went out for submissions for two further special issues:

• Time Series Econometrics
• Bayesian Econometrics

Judging by the quality of past special issues, these two will be ones to watch out for!

© 2013, David E. Giles