The chaotic, self-similar and hierarchical patterns in Bitcoin and Ethereum price series

Bitcoin (BTC) and Ethereum (ETH), pioneering public blockchains implementations, are two fundamental levers to register and transfer digital value. This article studies the structure of their daily price volatility time series following a multifaceted approach: first, it examines the existence of chaoticity and fractality in the time series. Obtained results confirm that the BTC and ETH price volatility series present signs of chaoticity, persistence of a long-term correlation and multifractality. Second, it analyses the corresponding visibility graphs associated with these time series using complex network theory. The undirected and connected complex networks, spawned by their natural visibility graphs (VGs) and horizontal visibility graphs (HVGs), present a hierarchical structure. These networks, especially the HVGs, confirm the fractality of the originating time series. The study of HVGs also confirms a lack of uncorrelated randomness in the originating BTC and ETH price series. This paper validates the value of visibility graphs as useful proxies to better understand complex time series, in this case, related to public blockchain implementations. •Bitcoin and Ethereum are fundamental levers to register and transfer digital value.•Multifaceted analysis of Bitcoin and Ethereum prices: time series & visibility graphs.•Bitcoin and Ethereum price series display chaoticity and multifractality.•Obtained visibility graphs display a hierarchy and hint fractality in original series.•Visibility graphs are useful proxies to better understand complex time series.