Solving the chaos model-data paradox in the cryptocurrency market

Abstract

In this paper we test for nonlinearity and chaos in some cryptocurrencies returns and volatility. Financial markets are characterized by the so-called chaos model-data paradox, that is, it is relatively easy to design theoretical dynamic financial models that behave chaotically, but it is hard to find robust evidence of this kind of chaotic behaviour in real dataset. In fact, this paradox has been taken as an evidence that support the Efficient Market Hypothesis (EMH). In this paper we apply new robust computational methods based on statistical procedures to reconstruct the underlying attractor and to estimate the Lyapunov exponents based on the Jacobian neural nets. We have tested nonlinearity and chaos in some digital cryptocurrencies (Bitcoin, Ethereum, Ripple and Litecoin). The results show strong evidence against EMH supporting the hypothesis that those time series come from an underlying unknown generating process that behave nonlinear and chaotically. This fact points out that a potential explication to the chaos model-data paradox lies in the methods traditionally used in the literature which are not robust and do not have the capability to find chaos in financial time-series data.