Analysis of inter-transaction time fluctuations in the cryptocurrency market

Abstract

We analyze tick-by-tick data representing major cryptocurrencies traded on some different cryptocurrency trading platforms. We focus on such quantities like the inter-transaction times, the number of transactions in time unit, the traded volume, and volatility. We show that the inter-transaction times show long-range power-law autocorrelations. These lead to multifractality expressed by the right-side asymmetry of the singularity spectra [Formula: see text] indicating that the periods of increased market activity are characterized by richer multifractality compared to the periods of quiet market. We also show that neither the stretched exponential distribution nor the power-law-tail distribution is able to model universally the cumulative distribution functions of the quantities considered in this work. For each quantity, some data sets can be modeled by the former and some data sets by the latter, while both fail in other cases. An interesting, yet difficult to account for, observation is that parallel data sets from different trading platforms can show disparate statistical properties.

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“…Moreover, a 'broom'-like shape of the function plots for different values of q may be interpreted as a signature of the multifractal nature of time series. This result goes in parallel to that previously reported for the mean number of transactions executed on different trading platforms [21]. For q = 2 we obtain the Hurst exponent H that serves as a measure of long-term autocorrelations.…”

“…The inter-transaction times and the number of transactions in the stock markets were reported to be multifractal [23,33] and the same was observed for the cryptocurrency market data [21]. Multiscaling of the related time series has also been reported with a strong indication that small fluctuations, i.e., the periods of increased trading frequency, show richer multifractality as compared to the large fluctuations associated with the periods of less frequent trading [21].…”

“…Only recently a progress in this direction has been reported in ref. [21], where the inter-transaction times, the number of transactions in unit time, and the traded volume have been analysed. Data representing major cryptocurrencies collected from a few trading platforms have shown that the inter-transaction times are long-term autocorrelated with a power-law decay [21] exactly as the data from the regular stock and Forex markets [22][23][24][25][26].…”

“…[21], where the inter-transaction times, the number of transactions in unit time, and the traded volume have been analysed. Data representing major cryptocurrencies collected from a few trading platforms have shown that the inter-transaction times are long-term autocorrelated with a power-law decay [21] exactly as the data from the regular stock and Forex markets [22][23][24][25][26]. This opens space for a future application and testing of the relevant stochastic models like the Markov switching multifractal duration model [26,27] and the continuous-time random walk model [28][29][30][31] to the cryptocurrency market data.…”

“…The long-term autocorrelations of inter-transaction times can also be responsible for their distribution tail behaviour, which according to the ref. [21] cannot be approximated by an exponentially decaying function but, in contrast, in many cases can be approximated by stretched exponential functions or the power-law ones.…”