The quantity Xk is subject to k blocking transformations. We now have d vectors X0,X1,⋯,Xd−1 containing the subsequent averages of observations. It turns out that if the components of X is a stationary time series, then the components of Xi is a stationary time series for all 0≤i≤d−1
We can then compute the autocovariance (or just covariance), the variance, sample mean, and number of observations for each i. Let γi,σ2i,¯Xi denote the covariance, variance and average of the elements of Xi and let ni be the number of elements of Xi. It follows by induction that ni=n/2i.