#### Technical Report USC-SIPI-125

“Recursive Method for Computation of Cumulants”

by Weizheng Wang and Jerry M. Mendel

April 1988

Recursive formulas for diagonal-slice cumulant computations of a state-variable model are developed. The computation formulas can be used for both stationary and non-stationary systems. The connection between stationary and non-stationary cumulant computations is also considered; it depends upon the assumption of an asymptotic stable model. This report is divided into two parts.

In Part I, a matrix formulation for third-order diagonal-slice cumulant computation is discussed. An ARMA model is given as an example which shows computation aspects of the methods. Results are also verified by analysis of AR and MA models.

In Part II, the Kronecker product is used to derive third- and fourth-order cumulant recursive computation formulas. Vector representations for third- and fourth-order cumulants are given and elegant recursive cumulant computation formulas are obtained.

Examples and simulations are given in both parts.

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