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Some Applications of Higher Moments of the Linear Gaussian White Noise Process
Department of Statistics, Federal University of Technology, Owerri, Nigeria
Department of Mathematics and Statistics, University of Portharcourt, Portharcourt, Nigeria
Department of Statistics, Federal University of Technology, Owerri, Nigeria
Department of Statistics, Federal University of Technology, Owerri, Nigeria
- 1 Department of Statistics, Federal University of Technology, Owerri, Nigeria
- 2 Department of Mathematics and Statistics, University of Portharcourt, Portharcourt, Nigeria
- 3 Department of Statistics, Federal University of Technology, Owerri, Nigeria
- 4 Department of Statistics, Federal University of Technology, Owerri, Nigeria
Applied Mathematics·Volume 08 (2017)·Pages 1918–1938·Published 4 December 2017·DOI10.4236/am.2017.812136
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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, σ 2 ) . Hence, if X 1 , x 2 , …, X n is a realization of such an iid sequence, this paper studies in detail the covariance structure of X 1 d , X 2 d , …, X n d , 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 X t d , d =2, 3, … can be used to distinguish between the Linear Gaussian white noise process and other processes with similar covariance structure.
KeywordsStochastic ProcessLinear Gaussian White Noise ProcessCovariance StructureStationarityTest for White Noise ProcessTest for Normality
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