Estimation of Parameters of Non-Gaussian Asymmetric Processes with a Moving Average Using the Polynomial Maximization Method PMM

Abstract

In this paper consider is the application of the Polynomial Maximization Method PMM to find estimates of the parameters of non-Gaussian Moving Average model. This approach is adaptive and is based on the analysis of higher-order statistics. The case of asymmetry of distributions of Moving Average of the stochastic processes is also considered. It is shown that the asymptotic variance of estimates of the Polynomial Maximization Method (2nd order) have such analytical expressions, whose allow to finding estimates and analyzing their uncertainties. Above approach can be significantly less than the variance of the classic estimates based on minimizing the Conditional Sum of Squares or Maximum Likelihood (in the Gaussian case). The increase of accuracy depends on the values of the coefficient’s asymmetry and the kurtosis of residuals. The results of statistical modeling by the Monte Carlo Method confirm the effectiveness of the proposed approach.