Fractal dynamics and wavelet analysis: deep volatility and returnproperties of Bitcoin, Ethereum and Ripple
2019
The substantial volatility and growth in cryptocurrencies valuations between 2009 and the end
of 2017 strongly suggest that both long memory and price volatility and return 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.
This research shows that Bitcoin prices exhibit long term memory, although its trend has been
reducing overtime. In fact, assessing Bitcoin, Ethereum and Ripple across the period between 2016
and 2017, focusing solely on the period prior to the crash of 2018, we can conclude that Bitcoin was
better described by a random walk, showing signs of markets maturity emerging, in contrast, other
cryptocurrencies such as Ethereum and Ripple present evidence of a growing underlying memory
behaviour.
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