We now define the blocking transformations. The idea is to take the mean of subsequent pair of elements from X and form a new vector X1. Continuing in the same way by taking the mean of subsequent pairs of elements of X1 we obtain X2, and so on. Define Xi recursively by:
(X0)k≡(X)k(Xi+1)k≡12((Xi)2k−1+(Xi)2k)for all1≤i≤d−1