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Some Applications of Higher Moments of the Linear Gaussian White Noise Process

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Document pages: 21 pages

Abstract: The Linear Gaussian white noise process is an independent and identicallydistributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such an iid sequence,this paper studies in detail the covariance structure of X1d, X2d, …, Xnd, d=1, 2, ….By this study, it is shown that: 1) all powers of a Linear Gaussian White NoiseProcess are iid but, not normally distributed and 2) the higher moments (varianceand kurtosis) of Xtd, d=2, 3, … can be used to distinguish betweenthe Linear Gaussian white noise process and other processes with similar covariancestructure.

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