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Fractional and fractal processes applied to cryptocurrencies price series
Journal of Advanced Research ( IF 11.4 ) Pub Date : 2021-01-07 , DOI: 10.1016/j.jare.2020.12.012
S A David 1 , C M C Inacio 1 , R Nunes 1 , J A T Machado 2
Affiliation  

Introduction

Cryptocurrencies have been attracting the attention from media, investors, regulators and academia during the last years. In spite of some scepticism in the financial area, cryptocurrencies are a relevant subject of academic research.

Objectives

In this paper, several tools are adopted as an instrument that can help market agents and investors to more clearly assess the cryptocurrencies price dynamics and, thus, guide investment decisions more assertively while mitigating risks.

Methods

We consider three methods, namely the Auto-Regressive Integrated Moving Average (ARIMA), Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) and Detrended Fluctuation Analysis, and three indices given by the Hurst and Lyapunov exponents or the Fractal Dimension. This information allows assessing the behaviour of the time series, such as their persistence, randomness, predictability and chaoticity.

Results

The results suggest that, except for the Bitcoin, the other cryptocurrencies exhibit the characteristic of mean reverting, showing a lower predictability when compared to the Bitcoin. The results for the Bitcoin also indicate a persistent behavior that is related to the long memory effect.

Conclusions

The ARFIMA reveals better predictive performance than the ARIMA for all cryptocurrencies. Indeed, the obtained residual values for the ARFIMA are smaller for the auto and partial auto correlations functions, as well as for confidence intervals.



中文翻译:

应用于加密货币价格系列的分数和分形过程

介绍

在过去几年中,加密货币一直吸引着媒体、投资者、监管机构和学术界的关注。尽管在金融领域存在一些怀疑,但加密货币是学术研究的一个相关主题。

目标

在本文中,采用了几种工具作为工具,可以帮助市场代理人和投资者更清楚地评估加密货币的价格动态,从而在降低风险的同时更果断地指导投资决策。

方法

我们考虑了三种方法,即自回归综合移动平均线 (ARIMA)、自回归分数综合移动平均线 (ARFIMA) 和去趋势波动分析,以及由 Hurst 和 Lyapunov 指数或分形维数给出的三个指数。该信息允许评估时间序列的行为,例如它们的持久性、随机性、可预测性和混乱性。

结果

结果表明,除比特币外,其他加密货币均表现出均值回归的特征,与比特币相比,可预测性较低。比特币的结果还表明与长记忆效应相关的持久行为。

结论

对于所有加密货币,ARFIMA 显示出比 ARIMA 更好的预测性能。实际上,对于自相关和偏自相关函数以及置信区间,获得的 ARFIMA 残差值较小。

更新日期:2021-01-07
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