Optimal estimates of MA and ARMA parameters of non-Gaussian processes from high-order cumulants

The authors describe an asymptotically minimum-variance algorithm for estimating the moving average (MA) and autoregressive moving average (ARMA) parameters of nonGaussian processes from sample second- and third-order moments. The algorithm uses the statistical properties (covariances and cross-covariances) of the sample moments explicitly. An alternative, simpler algorithm is also presented, which requires only linear operations. The latter algorithm is asymptotically minimum variance in the class of weighted least-squares algorithms