# AR(1) process can be estimated using linear regression

Can the $$AR(1)$$ process represented as $$x_t= ax_{t-1}+\epsilon_t$$ be estimated by regressing $$x_t$$ on its lagged value $$x_{t-1}$$.

• Yes, this is pretty standard. You can find this in most texbooks on AR models. – Richard Hardy Sep 16 at 7:30
• you can try it but you may get an estimate of $a$ whose absolute value is greater than 1.0. This invalidates the model the model as an AR(1) because it's not stationary. if you get an estimate for $a$ whose absolute value is less than 1.0, then you're okay. – mlofton Sep 16 at 8:11
• You should constrain your OLS linear regression to have a zero intercept. How to do this is software-package specific. @mlofton is right about stationarity. But this will work even in the explosive case with $|a|\ge 1$. – Peter Leopold Sep 16 at 12:44
• @Peter Leopold: That constraint is okay but it won't solve the issue that $|a|$ can come back greater than 1.0. – mlofton Sep 16 at 15:14