(a) Verify (5.52) for the MA(1) model. Hint: Use the fact that (lim Eleft(u^{prime} uight) /) ((N...
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(a) Verify (5.52) for the MA(1) model. Hint: Use the fact that \(\lim E\left(u^{\prime} uight) /\) \((N T)=\lim \operatorname{tr}(\Omega) /(N T)\) for deriving plim \(Q_{0}\). Similarly, use the fact that
\(\lim E\left(u^{\prime}\left(I_{N} \otimes G_{1}ight) uight) / N(T-1)=\lim \operatorname{tr}\left[\Omega\left(I_{N} \otimes G_{1}ight)ight] / N(T-1)\)
for deriving \(\operatorname{plim} Q_{1}\). Also,
\(\lim E\left(u^{\prime}\left(I_{N} \otimes G_{S}ight) uight) / N(T-s)=\lim \operatorname{tr}\left[\Omega\left(I_{N} \otimes G_{S}ight)ight] / N(T-s)\)
for deriving \(\operatorname{plim} Q_{s}\) for \(s=2, \ldots, S\).
(b) Verify (5.53) for the AR(1) model.
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