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We analyse tick-by-tick data representing major cryptocurrencies traded onsome different cryptocurrency trading platforms. We focus on such quantitieslike the inter-transaction times, the number of transactions in time unit, thetraded volume, and volatility. We show that the inter-transaction times showlong-range power-law autocorrelations. These lead to multifractality expressedby the right-side asymmetry of the singularity spectra $f(\alpha)$ indicatingthat the periods of increased market activity are characterised by richermultifractality compared to the periods of quiet market. We also show thatneither the stretched exponential distribution nor the power-law-taildistribution are able to model universally the cumulative distributionfunctions of the quantities considered in this work. For each quantity, somedata sets can be modeled by the former, some data sets by the latter, whileboth fail in other cases. An interesting, yet difficult to account for,observation is that parallel data sets from different trading platforms canshow disparate statistical properties.

Analysis of inter-transaction time fluctuations in the cryptocurrency market