On the topology of cryptocurrency markets

Abstract

Cryptocurrency markets are characterised by high volatility, high returns and comparative immaturity relative to equity and commodity markets. Topological Data Analysis (TDA) persistence norms are effective tools for the analysis of noisy dynamical systems like the cryptocurrency markets. We show how information from the shape of daily return data adds additional inference on activity within the cryptocurrency markets. TDA persistence norms embed volatility and connectedness between coins as well as incorporating information from uncertainty indexes, financial market performance and commodity returns. Our TDA measures are robust to noise and are consistent across a raft of alternative coin selections. Further, we exposit how persistence norms peak to forewarn of crashes and stay low as markets face exogenous shocks. We demonstrate the clear advantages of TDA for the study of cryptocurrency markets and develop the next steps for exploiting the potential of TDA for application to cryptocurrency markets.