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Nonstationarity of the mean and the hurst Phenomenon
Author(s) -
Boes Duane C.,
Salas Jose D.
Publication year - 1978
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr014i001p00135
Subject(s) - hurst exponent , phenomenon , autoregressive model , autoregressive–moving average model , econometrics , rescaled range , detrended fluctuation analysis , mathematics , statistical physics , statistics , physics , philosophy , epistemology , geometry , scaling
Hurst (1957), Klemeš (1974, 1975), and Potter (1975, 1976 a , 1976 b ) 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.