In the following linear AR (1) model, rt is the log price of a security at time t.

rt=0.00 4+rt−1+at,

here at is a random process obeying normal distribution N (µ, σ 2) with mean µ and variance σ 2, such as the following

at∼ iid N (0, 0.36),

Assume further that r100 = 3.865. Compute the 95% interval forecast for r101 at the forecast origin t = 100.