The blocking method was made popular by Flyvbjerg and Pedersen (1989) and has become one of the standard ways to estimate \( V(\widehat{\theta}) \) for exactly one \( \widehat{\theta} \), namely \( \widehat{\theta} = \overline{X} \).
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 time series is asymptotically uncorrelated. We switch to vector notation by arranging \( X_1,X_2,\cdots,X_n \) in an \( n \)-tuple. Define:
$$ \begin{align*} \hat{X} = (X_1,X_2,\cdots,X_n). \end{align*} $$The strength of the blocking method is when the number of observations, \( n \) is large. For large \( n \), the complexity of dependent bootstrapping scales poorly, but the blocking method does not, moreover, it becomes more accurate the larger \( n \) is.