Let xt evolve as the following AR(1) process: xt = αxt-1 + Ut (3) 0² where ut~ · WN(0,0²) and |a| < 1. Given the AR(1) s

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Let xt evolve as the following AR(1) process: xt = αxt-1 + Ut (3) 0² where ut~ · WN(0,0²) and |a| < 1. Given the AR(1) structure, the Long-Run Variance (LRV) of x‡ is known to be 12. Use the general formulation of the LRV of any station- (1-x)². ary and ergodic process, defined as: ∞ LRV = · γ(0) + 2 Σγ(j) (4) j=1 1 to verify, from first principles, that the LRV for the AR(1) in (3) is in fact · 0² (1-x)².