Is it valid to apply OLS to the AR process?
I learn that there exist correlation between explanatory variables and error term in AR model. I'm wondering how can show that $$E(u_t|x_t)\ne0$$,where vector of explanatory variable $x_t=(1, y_1,y_2,...,y_{t-1})$
And if AR model can not satisfy the assumption of BLUE, why OLS still used to estimate coefficient of AR model?
Statistical proof would be greatly appreciated, and if not, an intuition would be enough.
Remind that I'm looking for insights, not all the right answers.