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https://doi.org/10.1017/S0266466610000253

has been cited by the following article:

• TITLE: Some Applications of Higher Moments of the Linear Gaussian White Noise Process

  AUTHORS: I. S. Iwueze, C. O. Arimie, H. C. Iwu, E. Onyemachi

  KEYWORDS: Stochastic Process, Linear Gaussian White Noise Process, Covariance Structure, Stationarity, Test for White Noise Process, Test for Normality

  JOURNAL NAME: Applied Mathematics, Vol.8 No.12, December 29, 2017

  ABSTRACT: The Linear Gaussian white noise process is an independent and identically distributed (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 Noise Process are iid but, not normally distributed and 2) the higher moments (variance and kurtosis) of Xtd, d=2, 3, … can be used to distinguish between the Linear Gaussian white noise process and other processes with similar covariance structure.