Consider the second-order autoregressive, AR(2) process model, Zt=0.2+1.8Zt10.81Zt2+at, where the at is the Gaussian white noise with mean 0 and variance 4, and Z47 = 19, Z48 = 22, Z49 = 17, and Z50 = 21.

(c) find the forcasts

(d) find the 95% forecast limits in part (c)

(e) find the eventual forecast function for the forecast made at t=50 and its limiting value.