Verify the calculations made in Example 3.3: (a) Let xt = xt1 +wt where || > 1 and wt iid N(0, 2 w). Show

Verify the calculations made in Example 3.3:

(a) Let xt = φxt−1 +wt where |φ| > 1 and wt ∼ iid N(0, σ2 w). Show E(xt) = 0 and γx(h) = σ2 wφ−2 φ−h/(1 − φ−2).

(b) Let yt = φ−1yt−1 + vt where vt ∼ iid N(0, σ2 wφ−2) and φ and σw are as in part (a). Argue that yt is causal with the same mean function and autocovariance function as xt.