ARMA PARAMETER-ESTIMATION USING ONLY OUTPUT CUMULANTS

Several algorithms are developed to estimate the parameters of a causal nonminimum phase ARMA(p, q) system which is excited by an unobservable independent identically distributed (i.i.d.) non-Gaussian process; the output is contaminated by additive colored Gaussian noise of unknown power spectral density. First we present a fundamental result pertaining to the identifiability of AR parameters, based on the Yule-Walker type equations drawn from a (specific) set of (p + 1) 1-D slices of the kth (k > 2) order output cumulant. Next, we develop several MA parameter estimation algorithms: 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 also presented. A simulation study demonstrating the effectiveness of our algorithms is included. © 1990 IEEE