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.