Consider the stationary series generated by xt = + xt1 + wt + wt1, where E(xt) = , || < 1, || < 1

Consider the stationary series generated by xt = α + φxt−1 + wt + θwt−1, where E(xt) = µ, |θ| < 1, |φ| < 1 and the wt are iid random variables with zero mean and variance σ2 w.

(a) Determine the mean as a function of α for the above model. Find the autocovariance and ACF of the process xt, and show that the process is weakly stationary. Is the process strictly stationary?

(b) Prove the limiting distribution as n → ∞ of the sample mean, x¯ = n−1Xn t=1 xt, is normal, and find its limiting mean and variance in terms of α, φ, θ, and

σ2 w. (Note: This part uses results from Appendix A.)