Investigating Dynamical Complexity and Fractal Characteristics of Bitcoin/US Dollar and Euro/US Dollar Exchange Rates around the COVID-19 Outbreak

Abstract

This article investigates the dynamical complexity and fractal characteristics changes of the Bitcoin/US dollar (BTC/USD) and Euro/US dollar (EUR/USD) returns in the period before and after the outbreak of the COVID-19 pandemic. More specifically, we applied the asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) method to investigate the temporal evolution of the asymmetric multifractal spectrum parameters. In addition, we examined the temporal evolution of Fuzzy entropy, non-extensive Tsallis entropy, Shannon entropy, and Fisher information. Our research was motivated to contribute to the comprehension of the pandemic’s impact and the possible changes it caused in two currencies that play a key role in the modern financial system. Our results revealed that for the overall trend both before and after the outbreak of the pandemic, the BTC/USD returns exhibited persistent behavior while the EUR/USD returns exhibited anti-persistent behavior. Additionally, after the outbreak of COVID-19, there was an increase in the degree of multifractality, a dominance of large fluctuations, as well as a sharp decrease of the complexity (i.e., increase of the order and information content and decrease of randomness) of both BTC/USD and EUR/USD returns. The World Health Organization (WHO) announcement, in which COVID-19 was declared a global pandemic, appears to have had a significant impact on the sudden change in complexity. Our findings can help both investors and risk managers, as well as policymakers, to formulate a comprehensive response to the occurrence of such external events.

The Impact of COVID-19 on Weak-Form Efficiency in Cryptocurrency and Forex Markets

“…Therefore, we can conclude that investors adapted their investment decisions in response to the changing financial environment created mainly after the outbreak of the pandemic. Furthermore, this escalation in inefficiency within both BTC and EUR during the pandemic period aligns with the conclusions of a recent study [20], in which the authors documented a reduction in complexity and an augmentation in multifractality in both BTC and EUR returns. The heightened inefficiency further substantiates the notion that both returns exhibited reduced randomness following the outbreak of the pandemic.…”

“…This likely suggests that investors exhibited a more "organized" and similar behavior during this period, reducing the complexity of both markets. Corresponding results have been presented in the article [20]. Additionally, it is noteworthy that throughout the entire analysis period, BTC returns exhibited lower randomness than the corresponding EUR returns.…”

“…In particular, lower S q TS values characterize portions of the signal with lower complexity [46]. In this article, for the calculation of Tsallis entropy, we have chosen to use the value q TS = 1.8 for the non-extensive parameter, q TS , after [20,51].…”

“…The rescaled-range (R/S) analysis has been used to investigate the long-term memory of returns [18,19]. Various measures of entropy, such as fuzzy, approximate, Tsallis, and Shannon entropy, have been used to investigate the degree of disorder, randomness, and complexity of returns [20][21][22]. Detrended fluctuation analysis (DFA), multifractal detrended fluctuation analysis (MF-DFA), and asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) have been applied to detect the long-range correlations of returns.…”

“…Additionally, useful conclusions about the randomness of a time series can be obtained by studying its degree of multifractality. Specifically, the more random a time series is, the more unifractal its scaling, indicating that a more multifractal time series is farther from "randomness" [20,36]. Consequently, the methods outlined above are suitable for testing the efficient market hypothesis (EMH) in its weak form, as they can provide valuable information about the randomness of asset returns.…”