For the AR(1) model given in (5.26), show that if ρ0 and the xt ^' s are positively autocorrela

Question

For the AR(1) model given in (5.26), show that if ρ>0 and the xt ^' s are positively autocorrela

Accepted Answer

Step 1: Recall the AR(1) model given in equation (5.26):u000Au000A$$u000Ay_t u003D u005Cbeta_0 + u005Cbeta_1 x_t + u_tu000A$

For the AR(1) model given in (5.26), show that if $\rho>0$ and the $x_t{ }^{\prime} s$ are positively autocorrelated that $E\left(s^2 / \sum x_t^2\right)$ understates the var $\left(\hat{\beta}_{O L S}\right)$ given in (5.34).