Autoregression Model

Hi everyone,

Can anyone help me understand this fact : if the serie is Covariance stationary then : the absolute value of “b1” from AR(1) is less than 1. Thanks

From what I understand it should be b1<> 1 -(unit root issue), does in need to be less than 1?

There is a high level math for why it should not be greater than 1. So just for the sake , remember it that it can’t be greater than one when the series is cov. Stationary.

Talking about why it should not equal to one. We know the equation for calculating the mean reverting level of a dependent variable, which is =b0/(1-b1), so if the b1 = 1 then the mean reverting level will be undefined as in the denominator it will give zero. So, it is not cov. Stationary when the mean can’t be defined.

Hence b1 should be less than 1

Thank you for your answer, i ll just remember it :slight_smile: