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

HTML  XML Download Download as PDF (Size: 444KB)  PP. 1918-1938  
DOI: 10.4236/am.2017.812136    1,198 Downloads   3,125 Views  Citations

ABSTRACT

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.

Share and Cite:

Iwueze, I. , Arimie, C. , Iwu, H. and Onyemachi, E. (2017) Some Applications of Higher Moments of the Linear Gaussian White Noise Process. Applied Mathematics, 8, 1918-1938. doi: 10.4236/am.2017.812136.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.