We have
$$ \begin{align} \mathrm{var}(\overline{X}_k) = \frac{\sigma_k^2}{n_k} + \underbrace{\frac{2}{n_k} \sum_{h=1}^{n_k-1}\left( 1 - \frac{h}{n_k} \right)\gamma_k(h)}_{\equiv e_k} = \frac{\sigma^2_k}{n_k} + e_k \quad \text{if} \quad \gamma_k(0) = \sigma_k^2. \tag{4} \end{align} $$The term \( e_k \) is called the truncation error:
$$ \begin{equation} e_k = \frac{2}{n_k} \sum_{h=1}^{n_k-1}\left( 1 - \frac{h}{n_k} \right)\gamma_k(h). \tag{5} \end{equation} $$We can show that \( \mathrm{var}(\overline{X}_i) = \mathrm{var}(\overline{X}_j) \) for all \( 0 \leq i \leq d-1 \) and \( 0 \leq j \leq d-1 \).