(a) Using (5.3) and (5.4), verify that \(\Omega \Omega^{-1}=I\) and that \(\Omega^{-1 / 2} \Omega^{-1 / 2}=\Omega^{-1}\).

(b) Show that \(y^{*}=\sigma_{u} \Omega^{-1 / 2} y\) has a typical element \(y_{i t}^{*}=y_{i t}-\theta_{i} \bar{y}_{i}\). where \(\theta_{i}=1-\left(\sigma_{u} / \tau_{i}ight)\) and \(\tau_{i}^{2}=T w_{i}^{2}+\sigma_{u}^{2}\) for \(i=1, \ldots, N\).

Transcribed Image Text:

' = diag[(7)] JT + diag[(?)'] ET (5.3)