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

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Document pages: 22 pages

Abstract: Thelinear Gaussian white noise process (LGWNP) is an independent and identicallydistributed (iid) sequence with zeromean and finite variance with distribution . Some processes, such as the simple bilinear white noiseprocess (SBWNP), have the same covariance structure like the LGWNP. How canthese two processes be distinguished and or compared? If is a realization ofthe SBWNP. This paper studies in detail thecovariance structure of . It is shown from this study that; 1) the covariancestructure of is non-normal withdistribution equivalent to the linear ARMA(2, 1) model; 2) the covariance structure of is iid; 3) the variance of can be used for comparisonof SBWNP and LGWNP.

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