Analysis of instrumental methods for modeling stochastic processes in the economy

IF 0.4 Q4 MATHEMATICS, APPLIED
Maria G. Tindova, O. V. Ledneva
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引用次数: 0

Abstract

In this paper, the authors conduct a comparative analysis of instrumental methods used in modeling stochastic processes, namely, component analysis of time series, fractal modeling and modeling using p-adic mathematics. As an object of study, the authors chose the dynamics of the MICEX index. At the first step of the work, the authors carry out a detailed component analysis of the time series, which made it possible to identify the main development trend in the form of a quadratic function; periodic fluctuations with a period of six levels and a cyclical component describing fluctuations in the world economy with a period of fifty-five levels. At the second step of the work, the authors simulate the dynamics of the MICEX index using a fractal theory based on the self-similarity of the development of the economic process, which showed the ergodicity of the series under study with a stable influence of only the last twenty-four levels. The third step of the work was the p-adic modeling of the patterns existing in the series under study, which allowed the authors to reduce the model error to 6.8%. As a result of the work, a forecast of the dynamics of the MICEX exchange rate at four levels is presented, presented in three scenarios: optimistic, realistic and pessimistic. As conclusions of the work, an analysis was made of the possibility of using the considered methods for multiple, medium and long-term forecasts; the complexity of the methods and the need to use special software products are evaluated.
经济中随机过程建模的工具方法分析
本文对比分析了随机过程建模中常用的工具方法,即时间序列成分分析、分形建模和p进数学建模。笔者选择了MICEX指数的动态作为研究对象。在工作的第一步,作者对时间序列进行了详细的成分分析,从而可以以二次函数的形式确定主要的发展趋势;6级周期的周期性波动和55级周期的描述世界经济波动的周期性组成部分。在第二步工作中,作者利用基于经济过程发展自相似性的分形理论模拟了MICEX指数的动态,表明了所研究的序列的遍历性,并且仅对最后24个水平有稳定的影响。工作的第三步是对研究系列中存在的模式进行p-adic建模,这使得作者可以将模型误差降低到6.8%。作为工作的结果,提出了MICEX汇率在四个水平上的动态预测,提出了三种情况:乐观,现实和悲观。作为工作的结论,分析了使用所考虑的方法进行多次、中期和长期预测的可能性;评估了方法的复杂性和使用特殊软件产品的必要性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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CiteScore
0.70
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0.00%
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