Statistical properties and multifractality of Bitcoin

Abstract

Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at time scales shorter than one day and becomes consistent with zero at time scales longer than about one week. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models, and find no evidence of it. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are investigated, confirming that both temporal correlation and the fat-tailed distribution contribute to it. The influence of "Brexit" on June 23, 2016 to GBP-USD exchange rate and Bitcoin is examined in multifractal properties. We find that, while Brexit influenced the GBP-USD exchange rate, Bitcoin was robust to Brexit.

Rough volatility of Bitcoin

“…The Hurst exponent h(2) is estimated to be 0.144. This value is similar to those obtained for other assets(Gatheral , 2018;Bennedsen et al, 2016;Livieri et al, 2018). Table 1…”

Market Efficiency, Liquidity, and Multifractality of Bitcoin: A Dynamic Study

“…Based on the efficiency index, Kristoufek (2018) finds strong evidence that the Bitcoin markets remained mostly inefficient between 2010 and 2017. By analyzing one-minute returns from 2014 to 2016, Takaishi (2018) finds anti-persistence for high-frequency Bitcoin time series. Sensoy (2018) and Zargar and Kumar (2019) also report inefficiency of Bitcoin for high-frequency returns.…”

“…In addition, we calculate the generalized Hurst exponent, which characterizes the multifractal nature of the time series. The multifractality or generalized Hurst exponent of Bitcoin has also been addressed in the literature (Takaishi, 2018;Jiang et al, 2018;Al-Yahyaee et al, 2018;El Alaoui et al, 2018). Since Gaussian random time series show no multifractality, it has been suggested that the multifractal degree may be related to the degree to which a time series deviates from efficiency.…”

Seeking a Chaotic Order in the Cryptocurrency Market

“…The current literature on the cryptocurrency market is quite limited in the context of nonlinear behaviors of these instruments. The recent studies which discuss the chaotic dynamics of cryptocurrencies can be summarized as follows: Takaishi [33] and Lahmiri and Bekiros [34] independently studied the multifractality properties of bitcoin. Urquhart [35] studied the market inefficiency of bitcoin via random walks, whereas Bariviera [36] revisited the same topic by using Hurst exponent.…”