Abstract
THE behaviour of Hurst's1 range R is incompletely known, but it is evidently closely related to the standard deviation of the sum of N successive quantities, since the sums used in finding R are highly correlated. In fact, for a large number N of independent quantities, of standard deviation σ, R∝σ√N. If the quantities are correlated: 
where σ2
u(N) is the variance of mean of N successive quantities. If N is large the effect of differences between deviations from the measured mean and deviations from the true mean becomes small.
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References
Hurst, H. E., Nature, 180, 494 (1957).
Rice, S. O., Bell System Tech. J., 23, 282 (1944); 24, 46 (1945).
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PALMER, D. A Statistical Model of Some Time Series. Nature 181, 1677 (1958). https://doi.org/10.1038/1811677a0
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DOI: https://doi.org/10.1038/1811677a0
