The blocking method was made popular by Flyvbjerg and Pedersen (1989) and has become one of the standard ways to estimate the variance \( \mathrm{var}(\widehat{\theta}) \) for exactly one estimator \( \widehat{\theta} \), namely \( \widehat{\theta} = \overline{X} \), the mean value.
Assume \( n = 2^d \) for some integer \( d>1 \) and \( X_1,X_2,\cdots, X_n \) is a stationary time series to begin with. Moreover, assume that the series is asymptotically uncorrelated. We switch to vector notation by arranging \( X_1,X_2,\cdots,X_n \) in an \( n \)-tuple. Define:
$$ \begin{align*} \hat{X} = (X_1,X_2,\cdots,X_n). \end{align*} $$