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.
Highlights
A stochastic process Xt,t ∈ Z, where =Z {, −1, 0,1, } is called a white noise or purely random process, if with finite mean and finite variance, all the autocovariances are zero except at lag zero
This paper studies in detail the covariance structure of
That will help determine the values of β for which the simple bilinear model (1.20) is not distinguishable from the linear Gaussian white noise process (LGWNP)
Summary
A stochastic process Xt ,t ∈ Z , where =Z { , −1, 0,1, } is called a white noise or purely random process, if with finite mean and finite variance, all the autocovariances are zero except at lag zero. A stochastic process Xt ,t ∈ Z is called a linear Gaussian white noise if Xt ,t ∈ Z is a sequence of independent and identically distributed (iid) random variables with finite mean and finite variance. As noted by Iwueze et al [11], a stochastic process Xt ,t ∈ Z may have the covariance structure (1.1) through (1.5) even when it is not the linear Gaussian white noise process. Martins [16] obtained the autocorrelation function of the process for the simple bilinear model defined by (1.19) when et ,t ∈ Z is iid with a Gaussian distribution. 3) The series Xt ,t ∈ Z satisfying (1.21) has the same covariance structure as the linear Gaussian white noise processes. The covariance structure of=Yt is that of the linear white noise process
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
