The Hurst Effect

• H.E.Hurst worked on a variety of geographical time-series problems, particularly water storage.

  • Long-Term Storage Capacity of Reservoirs, 1951

• If the series is divided into non-overlapping blocks, the Rescaled Adjusted Range follows:

E[R(n)/S(n)] ~ cnH

• where the series is covariance-stationary, and

  • n is the block size
  • R is Max - Min value for the block
  • S is the Standard Deviation for the block
  • H is the Hurst parameter

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