It was with great interest that I read the paper by Kleme [1974] on the Hurst phenomenon, as I too have been exploring nonstationarity of the mean as a possible explanation of this phenomenon. The results, briefly summarized below, corroborate Kleme's demonstration that a series with a randomly shifting mean can exhibit the Hurst phenomenon with respect to the exponential increase of the rescaled range.
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Kenneth W. Potter (1975) studied this question.
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