Ethereum and Bitcoin: Analysis of Regression Relationships between Cryptocurrency Rates

Ksenofontov S.A.

Smolensk State University, faculty of Economics and Management, the Department of Mathematics and Informatics, Russia, 214004, Smolensk, Nikolayeva St. 25/31, Tel.: +79611359943, E-mail:

The similar dynamics of Ethereum and Bitcoin rates, as well as the high correlation coefficient of 0.84 (from 2017 to 2018) between the rates of these cryptocurrencies, raise the natural question: is there a causal relationship between the rates of Ethereum and Bitcoin, or the observed facts are only a consequence of a spurious regression caused by the trend, deterministic or stochastic, both variables. The cointegration model with the logarithms of the rates Ethereum and Bitcoin allows solving the problem. For the model, the Durbin-Watson statistics value is 0.01, which is less than 5% of the critical value. For the residuals, we obtain the value of Dickey-Fuller statistics, equal to -2.32, which is above the 5% critical level of -3.35. The criteria allow us to conclude about the spurious relationship between the considered time series and the absence of a long-run equilibrium between the rates of Ethereum and Bitcoin.

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