6.3 Simulate n = 100 observations from the following state-space model:

xt = .8xt−1 + wt and yt = xt + vt where x0 ∼ N(0, 2.78), wt ∼ iid N(0, 1), and vt ∼ iid N(0, 1) are all mutually independent. Compute and plot the data, yt, the one-stepahead predictors, yt−1 t along with the root mean square prediction errors, E1/2(yt − yt−1 t )2 using Figure 6.3 as a guide.