Abstract
This note illustrates that certain shifting level processes possess long‐term dependence and preserve the Hurst effect for the rescaled adjusted range. Although such processes belong to a stable domain of attraction, and not that of fractional Brownian motion, they do have asymptotic behavior of the rescaled adjusted range identical to that of fractional Brownian noise; further, they are easily simulated. Other shifting level processes belonging to the same stable domain of attraction preserve the Hurst effect for the raw and adjusted ranges but not for the rescaled adjusted range.
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