Chaos, randomness and multi-fractality in Bitcoin market

Since its inception, the digital currency market is considerably growing, especially in the most recent years. The main purpose of this paper is to investigate, assess and detect chaos, randomness, and multi-scale temporal correlation structure in prices and returns of this specific virtual and speculative market throughout two distinct time periods; namely under a low-level regime period during which prices slowly increased, and during a high and turbulent regime time period whereby they exponentially increased. We found that chaos is only present in prices during both periods, whilst the level of uncertainty in returns has significantly increased during the high-price time period. Furthermore, both prices and returns exhibit long-range correlations and multi-fractality. The fat-tailed probability distributions are the main source of multi-fractality in the time series of prices and returns. Finally, short (long) fluctuations in returns are dominant during low (high) price-regime time period, respectively. Overall, the high-price regime phase has profoundly revealed consistent nonlinear dynamical patterns in the Bitcoin market.