Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2019 018

Phenotypic convergence of cryptocurrencies

Daniel Traian Pele
Niels Wesselhöfft
Wolfgang K. Härdle
Michalis Kolossiatis
Yannis Yatracos

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

cryptocurrency, genus proximum, differentia specifica, classification,
multivariate analysis, factor models, phenotypic convergence, divergent

JEL Classification:
C14, C22, C46, C53, G32