Матеріали науково-практичних конференцій

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Browsing Матеріали науково-практичних конференцій by Subject "MATHEMATICS::Applied mathematics"

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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.
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    Polynomial Maximization Method for Estimation Parameters of Asymmetric Non-Gaussian Moving Average Models
    (Springer Nature, 2023) 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 Non-Gaussian Moving Average model. This approach is adaptive and is based on the analysis of higher-order statistics. Case of asymmetry of the distribution of Moving Average processes is considered. It is shown that the asymptotic variance of estimates of the Polynomial Maximization Method (2nd order) analytical expressions that allow finding estimates and analyzing their uncertainty are obtained. This approach can be significantly less than the variance of the classic estimates based on minimize Conditional Sum of Squares or Maximum Likelihood (in Gaussian case). The increase in accuracy depends on the values of the coefficient’s asymmetry and kurtosis of residuals. The results of statistical modeling by the Monte Carlo Method confirm the effectiveness of the proposed approach.