Phenotypic convergence of cryptocurrencies - Daniel Traian Pele; Niels Wesselhöfft; Wolfgang Karl Härdle; Michalis Kolossiatis; Yannis Yatracos (Humboldt-Universität zu Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series", 2019)
The aim of this paper is to prove the phenotypic convergence of cryptocurrencies, in the sense that individual cryptocurrencies respond to similar selection pressures by developing similar characteristics. In order to retrieve the cryptocurrencies phenotype, we treat cryptocurrencies as financial instruments (genus proximum) and find their specific difference (differentia specifica) by using the daily time series of log-returns. In this sense, a daily time series of asset returns (either cryptocurrencies or classical assets) can be characterized by a multidimensional vector with statistical components like volatility, skewness, kurtosis, tail probability, quantiles, conditional tail expectation or fractal dimension. By using dimension reduction techniques (Factor Analysis) and classification models (Binary Logistic Regression, Discriminant Analysis, Support Vector Machines, K-means clustering, Variance Components Split methods) for a representative sample of cryptocurrencies, stocks, exchange rates and commodities, we are able to classify cryptocurrencies as a new asset class with unique features in the tails of the log-returns distribution. The main result of our paper is the complete separation of the cryptocurrencies from the other type of assets, by using the Maximum Variance Components Split method. More, we observe a divergent evolution of the cryptocurrencies species, compared to the classical assets, mainly due to the tails behaviour of the log-returns distribution. The codes used here are available via www.quantlet.de.
Keywords: C14; C22; C46; C53; G32; 330; cryptocurrency; genus proximum; differentia specifica; classification; multivariate analysis; factor models; phenotypic convergence; divergent evolution