Author(s)

Christopher Onyema Arimie^1*, Iheanyi Sylvester Iwueze², Maxwell Azubuike Ijomah¹, Elechi Onyemachi²

¹Department of Mathematics and Statistics, University of Portharcourt, Portharcourt, Nigeria.
²Department of Statistics, Federal University of Technology, Owerri, Nigeria.

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.

White Noise Process, Normality, Stationarity, Invertibility, Covariance Structure

Arimie, C. , Iwueze, I. , Ijomah, M. and Onyemachi, E. (2018) On the Use of Second and Third Moments for the Comparison of Linear Gaussian and Simple Bilinear White Noise Processes. Open Journal of Statistics, 8, 562-583. doi: 10.4236/ojs.2018.83037.