Algorithms for optimal estimation of the parameters of non-Gaussian processes from high-order moments

The authors present several algorithms for estimating the parameters of MA (moving average) and ARMA (autoregressive moving average) non-Gaussian processes from sample high-order moments. These algorithms use explicitly the second-order statistics of the sample moments, which is estimated from the measurements. The asymptotically minimum-variance algorithms are shown, by numerical simulations, to perform close to theoretical predictions. The optimal weighted least-squares algorithms do not reach their theoretical performance, but they still offer some improvement over simpler algorithms. Since the computational load for the minimum variance algorithm is similar to that of the weighted least-squares algorithm, while its statistical accuracy is considerably higher, it is preferable to the weighted least-squares for most applications. The main disadvantage of the minimum variance algorithm is its more complex implementation (programming), especially the need for an iterative optimization procedure