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HIGHER ORDER MOMENTS OF SAMPLE AUTOCOVARIANCES AND SAMPLE AUTOCORRELATIONS FROM AN INDEPENDENT TIME SERIES
Author(s) -
Anderson Oliver D.,
Chen ZhaoGuo
Publication year - 1996
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1996.tb00280.x
Subject(s) - autocovariance , mathematics , independent and identically distributed random variables , autocorrelation , sample (material) , series (stratigraphy) , moment (physics) , gaussian , statistics , white noise , statistical physics , random variable , mathematical analysis , paleontology , chemistry , physics , chromatography , fourier transform , classical mechanics , quantum mechanics , biology
. Given length‐ n sampled time series, generated by an independent distributed process, in this paper we treat the problem of determining the greatest order, in n , that moments of the sample autocovariances and sample autocorrelations can attain. For the sample autocovariance moments, we achieve quite general results; but, for the autocorrelation moments, we restrict study to Gaussian white noise (normal, independent and identically distributed). Our main theorem relates to the cross‐moments of the non‐centred sample autocovariances, but we also establish a relation between these and the corresponding moments for the centred sample autocovariances.