Hi.

I have an auto-regressive process of order 1, AR(1). Assuming sample size n.

i) I would like to find, $\displaystyle Var(\bar{X})$ of AR(1). Would someone kindly show a source for this result? The correlation is denoted as $\displaystyle corr(X_i , X_j) = \rho^{|i-j|}$

ii) If the sample auto-correlation (lag 1) was about 0.25, how much an impact does that have on the standard error of $\displaystyle \bar{X}$, relative to the indpendence case?

Thank-you!