Statistical properties and multifractality of Bitcoin

TL;DR

This paper analyzes the statistical properties and multifractality of Bitcoin's 1-minute returns, revealing fat tails, slow convergence to Gaussian behavior, and multifractality driven by temporal correlations and fat-tailed distributions, with Bitcoin showing robustness to Brexit effects.

Contribution

It provides a comprehensive analysis of Bitcoin's statistical features and multifractality, highlighting the sources and robustness of Bitcoin's properties compared to traditional assets.

Findings

Bitcoin returns have fat-tailed distributions with slow Gaussian convergence.

Bitcoin exhibits multifractality influenced by temporal correlations and fat tails.

Bitcoin was unaffected by Brexit, unlike the GBP--USD exchange rate.

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.