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Methods of nonlinear dynamics as a hybrid tool for predictive analysis and research of risk-extreme levels

机译:非线性动力学方法作为混合工具进行风险极高水平的预测分析和研究

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The purpose of this research is to develop and adapt a complex of hybrid mathematical and instrumental methods of analysis and risk management through the prediction of natural time series with memory. The paper poses the problem of developing a constructive method for predictive analysis of time series within the current trend of using so-called “graphical tests” in the process of time series modeling using nonlinear dynamics methods. The main purpose of using graphical tests is to identify both stable and unstable quasiperiodic cycles (quasi-cycles). Modern computer technologies which allow to study in detail complex phenomena and processes were used as a toolkit for the implementation of nonlinear dynamics methods. Authors propose to use for the predictive analysis of time series a modified R / S -analysis algorithm, as well as phase analysis methods for constructing phase portraits in order to identify cycles of the studied time series and confirm the forecast. This approach differs from classical forecasting methods by implementing trends accounting and appears to the authors as a new tool for identifying the cyclical components of the considered time series. Using the proposed hybrid complex, the decision maker has more detailed information that cannot be obtained using classical statistics methods. In this paper, authors analyzed the time series of Kuban mountain river runoffs, revealed the impossibility of using the classical Hurst method for their predictive analysis and also proved the consistency of using the proposed hybrid toolkit to identify the cyclic components of the time series and predict it. The study acquires particular relevance in the light of the absence of any effective methods for predicting natural-economic time series, despite the proven need to study them and their risk-extreme levels. The work was supported by Russian Foundation for Basic Research (Grant No 17-06-00354 A).
机译:这项研究的目的是通过预测具有记忆的自然时间序列,开发和适应复杂的混合数学和工具分析与风险管理方法。本文提出了一个问题,即在使用非线性动力学方法进行时间序列建模的过程中,在当前趋势下,使用所谓的“图形测试”来开发一种用于时间序列预测分析的构造方法。使用图形测试的主要目的是识别稳定和不稳定的准周期周期(准周期)。允许详细研究复杂现象和过程的现代计算机技术被用作实现非线性动力学方法的工具包。为了对时间序列进行预测分析,作者建议使用一种改进的R / S分析算法,以及用于构造相像的相位分析方法,以识别研究时间序列的周期并确认预测。这种方法与传统的预测方法不同,它采用趋势会计方法,并在作者看来是一种用于识别所考虑的时间序列的周期性成分的新工具。使用建议的混合系统,决策者可以获得更详细的信息,而传统的统计方法则无法获得这些信息。在本文中,作者分析了库班山区河流径流的时间序列,揭示了使用经典赫斯特方法进行预测分析的可能性,并证明了使用所提出的混合工具包识别时间序列的循环分量并进行预测的一致性。它。鉴于没有任何有效的方法来预测自然经济时间序列,因此该研究具有特殊的意义,尽管已证明需要研究它们及其极端风险水平。这项工作得到了俄罗斯基础研究基金会(授权号17-06-00354 A)的支持。

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