ARMA parameter estimation using only output cumulants

Ananthram Swami, Jerry M. Mendel

Abstract: Several algorithms are developed to estimate the parameters of a causal nonminimum-phase autoregressive moving average (ARMA) (p,q) system which is excited by an unobservable independently identically distributed non-Gaussian process. The output is contaminated by additive colored Gaussian noise of unknown power spectral density. A fundamental result is presented pertaining to the identifiability of AR parameters, based on the Yule-Walker equations drawn from a (specific) set of (p+1) 1-D slices of the kth (k>2) order output cumulant. Several MA parameter estimation algorithms are developed: one method uses q 1-D slices of the output cumulant; a second method uses only two 1-D cumulant slices. These methods do not involve computation of the residual (i.e. AR compensated) time series or polynomial factorization. Multidimensional versions of the various algorithms are presented. A simulation study demonstrating the effectiveness of the algorithms is included.< >