Consider the AR(3) model
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and suppose that the observed data are
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where {et} and {at} are independent and the initial values of xj with j ≤ 0 are independent of et and at for t > 0.
(a) Convert the model into a state-space form.
(b) If E(et) = c, which is not zero, what is the corresponding state-space form for the system?