Fractional and fractal processes applied to cryptocurrencies price series

Autor(es)

David, S. A. ^[1] ; Inacio Jr, C. M. C. ; Nunes, R. ^[2] ; Machado, J. A. T. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Syst Dynam Grp, BR-13635900 Pirassununga, SP - Brazil

^[2] Inacio Jr, Jr., C. M. C., Univ Sao Paulo, Syst Dynam Grp, BR-13635900 Pirassununga, SP - Brazil

^[3] Inst Engn, Polytechn Porto, Rua Dr Antonio B Almeida 431, P-4249015 Porto - Portugal

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF ADVANCED RESEARCH; v. 32, n. SI, p. 85-98, SEP 2021.
• Citações Web of Science: 1

Resumo

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. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University. (AU)

• Processo FAPESP: 17/13815-3 - Dinâmica fracionária das séries de preços do etanol no Brasil
• Beneficiário: Sergio Adriani David
• Modalidade de apoio: Auxílio à Pesquisa - Programa BIOEN - Regular
• Processo FAPESP: 17/15517-0 - Comportamento dinâmico, no âmbito fracionário, das séries de preços de commodities agrícolas vis a vis os preços do etanol
• Beneficiário: Claudio Marcio Cassela Inacio Junior
• Modalidade de apoio: Bolsas no Brasil - Iniciação Científica