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

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    $\begingroup$ Yes, this is pretty standard. You can find this in most texbooks on AR models. $\endgroup$ – Richard Hardy Sep 16 at 7:30
  • $\begingroup$ 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. $\endgroup$ – mlofton Sep 16 at 8:11
  • $\begingroup$ 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 $|a|\ge 1$. $\endgroup$ – Peter Leopold Sep 16 at 12:44
  • $\begingroup$ @Peter Leopold: That constraint is okay but it won't solve the issue that $|a|$ can come back greater than 1.0. $\endgroup$ – mlofton Sep 16 at 15:14

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