Long Memory

In 1906, Harold Edwin Hurst, a young English civil servant, came to Cairo, Egypt, which was then under British rule. As a hydrological consultant, Hurst’s problem was to predict how much the Nile flooded from year to year. He developed a test for long-range dependence and found significant long-term correlations among fluctuations in the Nile’s outflows and described these correlations in terms of power laws. This statistic is known as the rescaled range, range over standard deviation or R/S statistic. From 1951 to 1956, Hurst, then in his seventies, published a series of papers describing his findings (Hurst, 1951). Hurst’s rescaled range (R/S) statistic is the range of partial sums of deviations of a time series from its mean, rescaled by its standard deviation.

Rescaled range analysis reveals whether or not a timeseries exhibits persistence or anti-persistence bias. Peters (Peters 1991) found long term persistent dependence with finite nonperiodic cycles in stock market indices, whilst several studies using Lo’s (Lo 1991) modified rescaled range statistic have contradicted Peters’ results.

Rescaled range analysis software in C++ NEW!

Excel spreadsheets which calculate the rescaled range statistic, or Hurst coefficient, listed below:




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