What's wrong if I fit the auto-regression with OLS? I am doing auto-regress by usual linear regression package.
e.g. 
$y_t=φx+ε_t$ with $x =y_{t-1}$
My reason is that,
Auto-regression does assumes iid errors, same for linear regression.
Linear Regression doesn't have assumption on independent variables.
What's different is merely that the independent variables is replaced with lagged dependent variable y.
But I see AR always is fitted by specific methods, I am afraid I'm doing wrong.
 A: To answer the title question, fitting an AR($p$) model using OLS will yield biased estimates. The reason is that for unbiasedness, the model errors should be uncorrelated with past, current and future values of regressors, which is not the case in autoregressive models. For example, in case of AR(1) 
$$ y_t=\varphi y_{t-1}+\varepsilon_t $$
(assuming zero mean for simplicity). Lag this by 1 to obtain 
$$ y_{t-1}=\varphi y_{t-2}+\varepsilon_{t-1}. $$
Note that $\varepsilon_{t-1}$ enters the model of $y_{t-1}$; hence, the regressor $y_{t-1}$ will be correlated with lagged error $\varepsilon_{t-1}$. The argument is given (without proof) e.g. in this lecture note, p. 5-6.
On a positive note, OLS gives consistent estimators for an autoregressive model (see the same lecture note, p. 4-5)
Also, in my experience OLS is quite popular for fitting AR models, and is pretty standard for fitting multivariate AR, i.e. VAR, models.
A: If you fit by regressing $\mathbf{y}_{p+1:n}=(y_{p+1},...,y_n)^\top$ on its lags $X=[\mathbf{y}_{p:n-1},\mathbf{y}_{p-1:n-2},...,\mathbf{y}_{1:n-p}]$ the lags of that on you're going to be conditioning on the first $p$ values (for an AR(p)). If you fit by say maximum likelihood you're able to incorporate the likelihood for the first $p$ values.
If $n$ is not very large relative to $p$ is can sometimes make a substantial difference.
