One Model Is Not Enough: Heterogeneity in Cryptocurrencies’ Multi-fractal Profiles

Abstract

This letter studies of the multi-fractal dynamics in 84 cryptocurrencies. It fills an important gap in the literature, by studying this market using two alternative multi-scaling methodologies. We find compelling evidence that cryptocurrencies have different degree of long range dependence, and — more importantly — follow different stochastic processes. Some of them follow models closer to mono-fractal fractional Gaussian noises, while others exhibit complex multi-fractal dynamics. Regarding the source of multi-fractality, our results are mixed. Time series shuffling produces a reduction in the level of multi-fractality, but not enough to offset it. We find an association of kurtosis with multi-fractality.

Keywords: Cryptocurrencies, Generalized Hurst Exponent, Multi-fractality, Efficient Market Hypothesis

JEL Classification: C4, G01, G14