Covarance Stationary

Dear all,

Why in AR model, we need covariance stationary?

I understand that covariance here is the cov(Xt, Xt-1) in AR(1). As, cov(Xt, Xt-1) is stationary we have X mean stationary and variance of X is stationary. Please advise if other

OLS (ordinary least square) regressions (even the modified versions) assume that the variables don’t have structural breaks and are covariance stationary, or at least are cointegrated (when they are not covariance stationary themselves, but their relationship is).

Since you use OLS regressions (or other versions of it) for AR models, you need the variable to be covariance stationary.

I know I may drawing a circular reference, but this assumption is pretty straightforward if you think at a simple example: Try to explain the movements of exchange rates (random movements) using the GDP growth rates. Is a non-sense. Exchange rates time-series are not covariance stationary and GDP growth rates are covariance stationary. The results of that regression is meaningless because errors of regression are simply astronomical compared to the portion successfully explained.

Thank you :slight_smile:

I thought that covariance stationary is only applied for times series ?