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.