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Statistical Properties of Multivariate Fractional Noise Processes
Author(s) -
Matalas N. C.,
Wallis J. R.
Publication year - 1971
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/wr007i006p01460
Subject(s) - mathematics , brownian motion , range (aeronautics) , fractional brownian motion , zero (linguistics) , statistical physics , infinity , sequence (biology) , domain (mathematical analysis) , flow (mathematics) , noise (video) , large deviations theory , stochastic process , statistics , mathematical analysis , physics , geometry , computer science , linguistics , materials science , philosophy , biology , composite material , genetics , image (mathematics) , artificial intelligence
Fractional noise processes belong to a class of stochastic processes that lie outside the Brownian domain of attraction. They are characterized by infinite memories and a parameter h that is the asymptotic slope of log ( R / S ) versus log N , where R is the range of cumulative departures from the sample mean, s is the sample standard deviation, and N is the sample size. The parameter h may be used to generate synthetic flows whose means, variances, skewnesses, lag one serial correlations, lag zero cross correlations, and h values are equal to those for historical flow sequences. Historical flow sequences yield values of h ≠ ½. Although Markovian processes, which belong to the Brownian domain, can preserve the values of the historical moments in the synthetic sequences, these processes generate sequences in which h tends to the value ½ as the sequence lengths tend to infinity.