Question: Again, consider the linear zero-mean ARMA(p, p) model of question 1. Let yt|h = E(yt y1, y2,, yh) be the conditional expectation of yt

Again, consider the linear zero-mean ARMA(p, p) model of question 1.

Let yt|h = E(yt ∣ y1, y2,…, yh) be the conditional expectation of yt given Fh = ????{y1,…, yh}, where h ≤ t. Let xt = (yt|t, yt+1|t,…, yt+p−1|t)′ be a pdimensional state vector. Derive an SSM for yt using the state variable xt.

This state space representation of ARMA models was proposed by Akaike

(1975).

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