MF-DCCA在金融时间序列中的应用概述指南：非平稳与平稳

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-08 DOI:10.1142/s0218348x23501050

Leonardo H. S. Fernandes, J. W. Silva, F. H. Araujo, Paulo A. M. Dos Santos, B. Tabak

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引用次数: 1

摘要

本文打破了多重分形方法在金融时间序列中的错误应用。具体来说，我们使用多重分形去趋势互相关分析(MF-DCCA)检验了圣保罗乙醇周价格时间序列与其他14个巴西首都相同生物燃料周价格时间序列之间的非线性互相关关系。鉴于平稳和非平稳金融时间序列的统计特性，我们建议采用多重分形方法来处理这些时间序列的两种可能性。我们的发现揭示并促进了基本时间序列分析技术和多重分形动力学之间的一致性。此外，我们发现MF-DCCA的使用受到时间序列选择(平稳或非平稳)的高度影响。

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Outlining guidelines for the application of the MF-DCCA in financial time series: non-stationary vs stationary

This paper disrupts mistaken applications of multifractal approaches in financial time series. Specifically, we have examined the non-linear cross-correlation between the São Paulo time series of the weekly price of ethanol and the other 14 Brazilian capitals’ time series of the weekly price of the same biofuel using the Multifractal Detrended Cross-Correlation Analysis (MF-DCCA). Given the statistical peculiars of stationary and non-stationary financial time series, we suggest two possibilities for employing multifractal approaches to these time series. Our findings shed light and promote alignment between basic time series analysis techniques and multifractal dynamics. Also, we discover that the use of MF-DCCA is highly impacted by choice of time series (stationary or non-stationary).

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.