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Digital assets termed cryptocurrencies are creating new paradigms for financial transactions as well as alternative means of capital. Despite their increasing relevance in financial situations, a complete understanding of the entire system remains lacking. Here the cryptocurrency market is treated as a complex system and analyzed using methods from statistical physics. The complexity–entropy causality plane (or CH plane) is employed in order to explore disorder and complexity in the space of cryptocurrencies. They are found to exist on distinct planar locations in the representation space, ranging from structured to stochastic-like behavior. The temporal trajectories of entropy and statistical complexity of prices vary drastically with position along the plane. Lastly cryptocurrencies appear to be characterized by ordinal patterns that represent strictly decreasing or increasing trends in price. The present analysis expands the understanding of and helps to quantify varying degrees of complexity in cryptocurrencies. • We map cryptocurrencies to the complexity–entropy causality plane. • We discover rather distinct degrees of complexity in the cryptocurrency space. • Their price behavior ranges from deterministic chaos to stochastic-like processes. • Most cryptocurrencies are characterized by downward or upward trends. [ABSTRACT FROM AUTHOR]

Abstract The cryptocurrency market has emerged in recent years with profound implications to central financial institutions such as banking. Bitcoin and other popular cryptocurrencies were recently analyzed using methods from statistical physics, but focus was exclusively on behavior of prices. Here we explore multifractal behavior of daily price changes and daily volume changes of fifty cryptocurrencies using the multifractal detrended fluctuation analysis (MF-DFA). Our results indicate that price changes are more complex than volume changes, and that large and small fluctuations dominate multifractal behavior of price and volume changes, respectively. We also find there is an absence of correlations in price changes, while volume changes present anti-persistent long-term correlations. Shuffling the series reveals that multifractality of both price and volume changes arises from a broad probability density function. The multifractal behavior of the cryptocurrency market is surprisingly similar to that of stock markets, but differs from that of regular exchange rates. Highlights • We discover common multifractal behavior in cryptocurrency exchanges. • Price changes and volume changes follow different multifractal dynamics. • Cryptocurrency market is similar to stock market but differs from regular currencies. [ABSTRACT FROM AUTHOR]

Digital assets termed cryptocurrencies are correlated. We analyze cross correlations between price changes of different cryptocurrencies using methods of random matrix theory and minimum spanning trees. We find that the cross correlation matrix exhibits non-trivial hierarchical structures and groupings of cryptocurrency pairs, which are not present in the partial cross correlations. In sharp contrast to the predictions for other financial markets, we discover that most of the eigenvalues in the spectrum of the cross correlation matrix do not agree with the universal predictions of random matrix theory, but the few of the largest eigenvalues deviate as expected. The minimum spanning tree of cryptocurrency cross correlations reveals distinct community structures that are surprisingly stable. Collective behaviors that are present in the cryptocurrency market can be useful for the construction of portfolio of cryptocurrencies as well as for future research on the subject. [ABSTRACT FROM AUTHOR]

Cryptocurrencies represent a new type of financial assets that are traded in a decentralized and transparent way. Recently, cryptocurrencies with large market capitalization (mostly Bitcoin) have been studied theoretically, but a deeper understanding of their underlying mechanisms remains elusive. Here we explore the nonextensivity of price changes for 20 cryptocurrency exchanges from 2013 until 2017. We discover nonextensive triplets in the cryptocurrency market, where the three associated values for Bitcoin are remarkably close to those of the logistic map near the edge of chaos. The current findings strongly indicate that the cryptocurrency market represents a system whose physics is properly described by nonextensive statistical mechanics. Our results shed light on the complex and volatile nature of cryptocurrencies, and establish the first formal link with the nonextensive theory. [ABSTRACT FROM AUTHOR]