It has become vital to effectively characterize the self-similar and regular patterns in time series marked by short-term and long-term memory in various fields in the ever-changing and complex global landscape. Within this framework, attempting to find solutions with adaptive mathematical models emerges as a major endeavor in economics whose complex systems and structures are generally volatile, vulnerable and vague. Thus, analysis of the dynamics of occurrence of time section accurately, efficiently and timely is at the forefront to perform forecasting of volatile states of an economic environment which is a complex system in itself since it includes interrelated elements interacting with one another. To manage data selection effectively and attain robust prediction, characterizing complexity and self-similarity is critical in financial decision-making. Our study aims to obtain analyzes based on two main approaches proposed related to seven recognized indexes belonging to prominent countries (DJI, FCHI, GDAXI, GSPC, GSTPE, N225 and Bitcoin index). The first approach includes the employment of Hurst exponent (HE) as calculated by Rescaled Range ([Formula: see text]) fractal analysis and Wavelet Entropy (WE) in order to enhance the prediction accuracy in the long-term trend in the financial markets. The second approach includes Artificial Neural Network (ANN) algorithms application Feed forward back propagation (FFBP), Cascade Forward Back Propagation (CFBP) and Learning Vector Quantization (LVQ) algorithm for forecasting purposes. The following steps have been administered for the two aforementioned approaches: (i) HE and WE were applied. Consequently, new indicators were calculated for each index. By obtaining the indicators, the new dataset was formed and normalized by min-max normalization method’ (ii) to form the forecasting model, ANN algorithms were applied on the datasets. Based on the experimental results, it has been demonstrated that the new dataset comprised of the HE and WE indicators had a critical and determining direction with a more accurate level of forecasting modeling by the ANN algorithms. Consequently, the proposed novel method with multifarious methodology illustrates a new frontier, which could be employed in the broad field of various applied sciences to analyze pressing real-world problems and propose optimal solutions for critical decision-making processes in nonlinear, complex and dynamic environments.

中文翻译：

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基于自相似时间序列建模的鲁棒预测R/S分形分析和小波熵表征方法

在瞬息万变和复杂的全球格局中，有效地刻画时间序列中以短期和长期记忆为标志的自相似和规律模式变得至关重要。在此框架内，尝试使用自适应数学模型寻找解决方案成为经济学中的一项重大努力，其复杂的系统和结构通常是不稳定的、脆弱的和模糊的。因此，准确、高效和及时地分析时间段发生的动态对于预测经济环境的波动状态是最重要的，因为它本身就是一个复杂的系统，因为它包括相互影响的相互关联的元素。为了有效地管理数据选择并获得稳健的预测，表征复杂性和自相似性在财务决策中至关重要。我们的研究旨在基于与属于主要国家的七个公认指数（DJI、FCHI、GDAXI、GSPC、GSTPE、N225 和比特币指数）相关的两种主要方法进行分析。第一种方法包括使用由 Rescaled Range（[公式：见文本]）分形分析和小波熵 (WE) 计算的赫斯特指数 (HE)，以提高对金融市场长期趋势的预测准确性. 第二种方法包括用于预测目的的人工神经网络 (ANN) 算法应用前馈反向传播 (FFBP)、级联前向反向传播 (CFBP) 和学习向量量化 (LVQ) 算法。已针对上述两种方法执行了以下步骤：(i) 应用了 HE 和 WE。因此，为每个指标计算了新指标。通过获得指标，形成新的数据集并通过最小-最大归一化方法进行归一化'（ii）以形成预测模型，将ANN算法应用于数据集。实验结果表明，由 HE 和 WE 指标组成的新数据集具有关键和决定性的方向，具有更准确的 ANN 算法预测建模水平。因此，所提出的具有多种方法的新方法说明了一个新的前沿，可用于各种应用科学的广泛领域，以分析紧迫的现实世界问题，并为非线性、复杂和动态环境中的关键决策过程提出最佳解决方案.