Fractal Dynamics and Wavelet Analysis: Deep Volatility Properties of Bitcoin, Ethereum and Ripple

Abstract

The substantial growth of the crytocurrency market since 2009 has merited suspicions of bubblelike dynamics attributed to the exceptional price growth and volatility exhibited across associated exchanges. The deep volatility and exponential rise in cryptocurrencies valuations strongly suggest that both long memory and price volatility spillovers should be present in these assets dynamics. To date, literature on the major cryptocurrencies price processes does not address jointly and comprehensively their fractal properties, long memory and wavelet analysis, that could robustly confirm the presence of fractal dynamics in their prices, and confirm or deny the validity of the Fractal Market Hypothesis as being applicable to the cryptocurrencies. Having performed both analyses, our overall results that Bitcoin prices show persistency. This trend has been reducing overtime. Assessing the period 2016 between 2017, Bitcoin is better described by a random walk while less mature cryptocurrencies such as Ethereum and Ripple present evidence of persistence behaviour, and may be better described as a random walk. We conclude that Bitcoin may be described as a ‘True Hurst Process’, where crowd behaviour and technical information tend to dominate the leading cryptocurrency’s price development.