Loading [MathJax]/extensions/TeX/boldsymbol.js

 

 

 

Resampling methods: Blocking

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*}