Abstract

As stated in the short note by R. O. Plaisted and H. G. Peña, they derived what they believed to be “a maximum entropy (MEM) representation for bispectra” and they claimed that their result “can be generalized to an Nth-order MEM auto-spectrum.” The purpose of this discussion is to point out the faults in the derivation and show that the claim of MEM is not correct. Furthermore, the parametric representation of the bispectrum that the authors actually attempted to derive is not new but can be found elsewhere (Huber et al., 1971).

Plaisted and Peña stated that the random variables {εt} in their equation (1) can be assumed generally to be normally distributed with zero mean and variance σε2. This is a serious mistake. With this assumption the third?order moment sequence of the {xt} process given by their equation (3) vanishes, i.e., γk,l = 0 for all (k, l) and therefore the bispectrum of {xt} is identical to zero. The random variables {εt} in their equation (1) and hence {xt} have to be non-Gaussian for the bispectrum of {xt} to exist. As a matter of fact, bispectral analysis has been used to obtain information regarding deviations of a process from Gaussianity (Godfrey, 1965).

This content is PDF only. Please click on the PDF icon to access.

First Page Preview

First page PDF preview
You do not currently have access to this article.