The rescaled adjusted range statistic, 
, is
calculated for a selection of subsets of the time series 
,
starting at n and of size k+1 [Mandelbrot 1969]. The adjusted range
has the following physical interpretation. Suppose the time series
represents the amounts of water per time unit flowing into a reservoir.
Furthermore, water flows out of the reservoir at a constant rate, this rate
being just such that the reservoir contains the same amount of water at the
n+k-th time unit as at the n-th time unit. Then 
is the minimum
capacity of the reservoir such that it will not overflow in the period n to
n+k inclusive.
The calculation of 
proceeds as follows. Given n and k, the mean
and standard deviation
are calculated. Then,
is found. The rescaled adjusted range is then just 
.
A single such calculation results in one point on a graph of
against 
. By varying n and
k we obtain a pox plot of 
. The
size k is varied from 10 to about 
in 5,000 logarithmically-spaced
steps (except for small k, where several calculations of 
are
made for the same k and different n). The starting value n is chosen
randomly in the range 1 to N-k. Finally, linear regression is used
to fit a straight line to the 
plot, the slope of this line being
an estimate of H.