Kwapień Jarosław, Wątorek Marcin, Bezbradica Marija, Crane Martin, Tan Mai Tai, Drożdż Stanisław
Department of Complex Systems Theory, Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Kraków, Poland.
Faculty of Computer Science and Telecommunications, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland.
Chaos. 2022 Aug;32(8):083142. doi: 10.1063/5.0104707.
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 f ( α ) 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.
我们分析了在一些不同加密货币交易平台上交易的主要加密货币的逐笔数据。我们关注诸如交易间隔时间、单位时间内的交易数量、交易量和波动性等数量。我们表明，交易间隔时间呈现出长程幂律自相关性。这些导致了由奇异谱f(α)的右侧不对称性所表示的多重分形性，这表明与市场平静时期相比，市场活动增加的时期具有更丰富的多重分形性。我们还表明，拉伸指数分布和幂律尾部分布都不能普遍地对本工作中考虑的数量的累积分布函数进行建模。对于每个数量，一些数据集可以由前者建模，一些数据集可以由后者建模，而在其他情况下两者都失败。一个有趣但难以解释的观察结果是，来自不同交易平台的并行数据集可能显示出不同的统计特性。
