On the Use of Second and Third Moments for the Comparison of Linear Gaussian and Simple Bilinear White Noise Processes

• 作者: Christopher Onyema Arimie Elechi Onyemachi Iheanyi Sylvester Iwueze Maxwell Azubuike Ijomah
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: White Noise Process NORMALITY Stationarity INVERTIBILITY COVARIANCE Structure
• 年，卷（期）: 2018,（3）
• 页码范围: 562-583
• 页数: 22页
• 分类号: O1

摘要

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.