TITLE:
On the Use of Second and Third Moments for the Comparison of Linear Gaussian and Simple Bilinear White Noise Processes
AUTHORS:
Christopher Onyema Arimie, Iheanyi Sylvester Iwueze, Maxwell Azubuike Ijomah, Elechi Onyemachi
KEYWORDS:
White Noise Process, Normality, Stationarity, Invertibility, Covariance Structure
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.3,
June
15,
2018
ABSTRACT: The
linear Gaussian white noise process (LGWNP) is an independent and identically
distributed (iid) sequence with zero
mean and finite variance with distribution . Some processes, such as the simple bilinear white noise
process (SBWNP), have the same covariance structure like the LGWNP. How can
these two processes be distinguished and/or compared? If is a realization of
the SBWNP. This paper studies in detail the
covariance structure of . It is shown from this study that; 1) the covariance
structure of is non-normal with
distribution equivalent to the linear ARMA(2, 1) model; 2) the covariance structure of is iid; 3) the variance of can be used for comparison
of SBWNP and LGWNP.