Nonstationarity of the mean and the hurst Phenomenon

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Abstract
Hurst (1957), Klemeš (1974, 1975), and Potter (1975, 1976a, 1976b) show that nonstationarity of the mean provides a possible explanation of the so‐called Hurst phenomenon; O'Connell (1971) and Wallis and O'Connell (1973 )show that this phenomenon can also be explained with a mixed autoregressive‐ moving average (Arma) process. These two alternate explanations can be quite similar; in fact, both Hurst's (1957) model and a model suggested by Klemeš (1974) and Potter (1975) have correlation structure identical to an Arma (1,1) process. A mixture model for shifting levels is proposed, and it is shown that the models of Hurst and Klemeš and Potter are special cases.