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Moments of the sampled autocovariances and autocorrelations for a Gaussian white‐noise process
Author(s) -
Anderson Oliver D.
Publication year - 1990
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315458
Subject(s) - cumulant , autocorrelation , white noise , mathematics , moment (physics) , gaussian , gaussian noise , noise (video) , statistical physics , additive white gaussian noise , series (stratigraphy) , method of moments (probability theory) , statistics , algorithm , physics , computer science , quantum mechanics , artificial intelligence , image (mathematics) , paleontology , estimator , biology
Abstract Cumulants, moments about zero, and central moments are obtained for the mean‐corrected serial covariances and serial correlations for series realizations of length n from a white‐noise Gaussian process. All first and second moments (and some third, fourth, and higher moments) are given explicitly for the serial covariances; and the corresponding moments for the serial correlations are derived either explicitly or implicitly.