The quantity \boldsymbol{X}_k is subject to k blocking transformations. We now have d vectors \boldsymbol{X}_0, \boldsymbol{X}_1,\cdots,\boldsymbol{X}_{d-1} containing the subsequent averages of observations. It turns out that if the components of \boldsymbol{X} is a stationary time series, then the components of \boldsymbol{X}_i is a stationary time series for all 0 \leq i \leq d-1
We can then compute the autocovariance (or just covariance), the variance, sample mean, and number of observations for each i . Let \gamma_i, \sigma_i^2, \overline{X}_i denote the covariance, variance and average of the elements of \boldsymbol{X}_i and let n_i be the number of elements of \boldsymbol{X}_i . It follows by induction that n_i = n/2^i .