Some long‐run properties of geophysical records

Abstract

A variety of geophysical records are examined to determine the dependence upon the lag s of a quantity called ‘rescaled range,’ denoted by R ( t , s )/ S ( t , s ). If there had been no appreciable dependence between two values of the record at very distant points in time, the ratio R / S would have been proportional to s 0.5 . But, in fact, as first noted by Edwin Hurst, the R / S ratio of hydrological and other geophysical records is proportional to s H with H ≠ 0.5. Hurst's original claims must be tightened and hedged, and his estimates of H must be discarded, but his general idea will be shown to be correct. We have shown elsewhere that this behavior of R / S means that the strength of long‐range statistical dependence in geophysical records is considerable.