Prove that the optimal interpolation of the vector process ((boldsymbol{I}-boldsymbol{Phi} B) boldsymbol{z}_{t}=boldsymbol{a}_{t}) at time (t=h) is given

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Prove that the optimal interpolation of the vector process \((\boldsymbol{I}-\boldsymbol{\Phi} B) \boldsymbol{z}_{t}=\boldsymbol{a}_{t}\) at time \(t=h\) is given by \(\widehat{z}_{h}=\left(\boldsymbol{I}+\boldsymbol{\Phi}^{\prime} \boldsymbol{\Phi}\right)^{-1} \boldsymbol{\Phi}\left(z_{h-1}+z_{h+1}\right)\).

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