2022 рік

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Application of the Polynomial Maximization Method for Estimation Parameters of Autoregressive Models with Asymmetric Innovations
(Springer Nature, 2022) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Tkachenko, Oleksandr; Warsza, Zygmunt Lech
This paper considers the application of the Polynomial Maximization Method to find estimates of the parameters of autoregressive model with non-Gaussian innovation. This approach is adaptive and is based on the analysis of higher-order statistics. Analytical expressions that allow finding estimates and analyzing their uncertainty are obtained. Case of asymmetry of the distribution of autoregressive innovations is considered. It is shown that the variance of estimates of the Polynomial Maximization Method can be significantly less than the variance of the estimates of the linear approach (based on Yule-Walker equation or Ordinary Least Squares). The increase in accuracy depends on the values of the cumulant coefficients of higher orders of innovation residuals. The results of statistical modeling by the Monte Carlo method confirm the effectiveness of the proposed approach.