8. The logarithm of $$ e_{1, t|t}^{T}e_{1, t|t} $$, $$ (e_{t|t}^{g})^{T}e_{t|t}^{g} $$, $$ \text{tr}(\bar{P}_{1, t\mid t}) $$ and $$ \text{tr}(\bar{P}_{t\mid t}^g) $$.
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