Question: Consider the state-space model presented in Example 6.3. Let xt1 t = E(xt|yt1, . . . , y1) and let Pt1 t = E(xt

Consider the state-space model presented in Example 6.3. Let xt−1 t =

E(xt|yt−1, . . . , y1) and let Pt−1 t = E(xt − xt−1 t )2. The innovation sequence or residuals are t = yt − yt−1 t , where yt−1 t = E(yt|yt−1, . . . , y1). Find cov(s, t)

in terms of xt−1 t and Pt−1 t for (i) s 6= t and (ii) s = t.

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