Mark, MichaelSila, JanWeber, Thomas A.2020-07-012020-07-012020-07-01202210.1080/1351847X.2020.1791925https://infoscience.epfl.ch/handle/20.500.14299/169727We construct a ‘reflexivity’ index to measure the activity generated endogenously within a market for cryptocurrencies. For this purpose, we fit a univariate self-exciting Hawkes process with two classes of parametric kernels to high-frequency trading data. A parsimonious model of both endogenous and exogenous dynamics enables a direct comparison with exchanges for traditional asset classes, in terms of identified branching ratios. We also formulate a ‘Hawkes disorder problem,’ as a generalization of the established Poisson disorder problem, and provide a simulation-based approach to determining an optimal observation horizon. Our analysis suggests that Bitcoin mid-price dynamics feature long-memory properties, well explained by the power-law kernel, at a level of criticality similar to the fiat-currency market.bitcoinbranching ratiocryptocurrenciesendogeneityHawkes processmaximum-likelihood estimationtext::journal::journal article::research article