Question: Simulate n = 100 observations from the following state-space model: xt = .8xt1 + wt and yt = xt + vt where x0 N(0,

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-step-ahead 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.

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