Some Applications of Higher Moments of the Linear Gaussian White Noise Process

• 作者: C. O. Arimie E. Onyemachi H. C. Iwu I. S. Iwueze
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Stochastic PROCESS LINEAR Gaussian WHITE Noise PROCESS COVARIANCE Structure Stationarity TEST for WHITE Noise PROCESS TEST for NORMALITY
• 年，卷（期）: 2017,（12）
• 页码范围: 1918-1938
• 页数: 21页
• 分类号: O1

摘要

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.