Wavelet Entropy and Complexity Analysis of Cryptocurrencies Dynamics

Cryptocurrencies emerged almost one decade ago, as an alternative peer-to-peer payment method. Even though their currency characteristics have been challenged by several researchers, they constitute an important speculative financial asset. This paper examines the long memory properties in high frequency (5 min) time series of eight important cryptocurrencies. We perform a statistical analysis of two key financial characteristics of time series: return and volatility. We compute information theory quantifiers using a wavelet decomposition of the time series: wavelet entropy and wavelet statistical complexity of returns and volatility of each time series. We find two important features in the time series: (i) high frequency returns exhibit a trend toward a more efficient behavior, and (ii) high frequency volatility reflects a strong persistence in volatility. Both findings have important implications for portfolio managers, and investors in general. The presence of persistent volatility validates the use of GARCH-type models. Thus, understanding volatility could create opportunities for short-term day traders.