Time-varying properties of asymmetric volatility and multifractality in Bitcoin (original) (raw)
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Market Efficiency, Liquidity, and Multifractality of Bitcoin: A Dynamic Study
Asia-pacific Financial Markets, 2019
This letter investigates the dynamic relationship between market efficiency, liquidity, and multifractality of Bitcoin. We find that before 2013 liquidity is low and the Hurst exponent is less than 0.5, indicating that the Bitcoin time series is anti-persistent. After 2013, as liquidity increased, the Hurst exponent rose to approximately 0.5, improving market efficiency. For several periods, however, the Hurst exponent was found to be significantly less than 0.5, making the time series anti-persistent during those periods. We also investigate the multifractal degree of the Bitcoin time series using the generalized Hurst exponent and find that the multifractal degree is related to market efficiency in a non-linear manner.
Statistical properties and multifractality of Bitcoin
Physica A: Statistical Mechanics and its Applications
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.
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Bitcoin has recently been labelled as a “dangerous speculative bubble†by Nobel Prize-winning economists Joseph Stiglitz and Robert Shiller, as the Bitcoin's market value now exceeds the GDP of over 130 countries. In this study, the multifractality and efficiency of the Bitcoin price index are tested, using a nonlinear data analysis technique called the multifractal detrended fluctuation analysis (MF-DFA). In addition, we assess the time-variations in the market efficiency level through using a rolling-window framework. Our evidence shows that the efficiency of the Bitcoin market changes over time and this market seems to be more efficient during downward than upward periods. We also find that Bitcoin is marked by a persistent long memory phenomenon in its short- term components, which could be interpreted as a possible speculation by investors.
Future Internet
Unlike price fluctuations, the temporal structure of cryptocurrency trading has seldom been a subject of systematic study. In order to fill this gap, we analyse detrended correlations of the price returns, the average number of trades in time unit, and the traded volume based on high-frequency data representing two major cryptocurrencies: bitcoin and ether. We apply the multifractal detrended cross-correlation analysis, which is considered the most reliable method for identifying nonlinear correlations in time series. We find that all the quantities considered in our study show an unambiguous multifractal structure from both the univariate (auto-correlation) and bivariate (cross-correlation) perspectives. We looked at the bitcoin–ether cross-correlations in simultaneously recorded signals, as well as in time-lagged signals, in which a time series for one of the cryptocurrencies is shifted with respect to the other. Such a shift suppresses the cross-correlations partially for short t...
Multifractal behavior in return and volatility series of Bitcoin and gold in comparison
Chaos Solitons & Fractals, 2020
In this study, we investigate multifractal nature of return and volatility (proxied by absolute and squared returns) series of Bitcoin and gold throughout full sample periods and sub-sample periods which are decided accordingly the results of the structural breaks in the full sample periods. Applying the Multifractal Detrended Fluctuation Analysis (MFDFA), it is found that Bitcoin return series have distinctly different multifractal properties than of gold. Our evidence shows that all return and volatility series of Bitcoin have a persistent behavior, and have higher degree of multifractality than of gold. Using rolling windows approach, we confirm the persistence and the higher degree of multifractality of Bitcoin time series. Return series of gold have uncorrelated behavior while volatility series of gold have persistent behavior. Moreover, applying structural break test for the series of complexity parameters retrieved from the multifractal analysis of the return and volatility series of gold and Bitcoin, our results indicate that time series of gold have different regimes with different characteristics of multifractality. Furthermore, impact of temporal correlations and fat-tails is also examined and both are found to be the source of multifractality in the return series of Bitcoin and gold. In volatility series of Bitcoin, multifractality arises mostly due to long-range correlations and fat-tails. However, presence of long-range correlations and fat-tails in the original volatility series of gold mostly yields to less degree of multifractality.
Some stylized facts of the Bitcoin market
In recent years a new type of tradable assets appeared, generically known as cryptocurrencies. Among them, the most widespread is Bitcoin. Given its novelty, this paper investigates some statistical properties of the Bitcoin market. This study compares Bitcoin and standard currencies dynamics and focuses on the analysis of returns at different time scales. We test the presence of long memory in return time series from 2011 to 2017, using transaction data from one Bitcoin platform. We compute the Hurst exponent by means of the Detrended Fluctuation Analysis method, using a sliding window in order to measure long range dependence. We detect that Hurst exponents changes significantly during the first years of existence of Bitcoin, tending to stabilize in recent times. Additionally, multiscale analysis shows a similar behavior of the Hurst exponent, implying a self-similar process.
Price Appreciation and Roughness Duality in Bitcoin: A Multifractal Analysis
Mathematics, 2021
Since its launch in 2009, bitcoin has thrived, attracting the attention of investors, regulators, academia, and the public in general. Its price dynamics, characterized by extreme volatility, severe jumps, and impressive long-term appreciation, suggest that bitcoin is a new digital asset. This study presents a comprehensive overview of the fractality of bitcoin in a high-frequency framework, namely by applying Multifractal Detrended Fluctuation Analysis (MF-DFA) and a Multifractal Regime Detecting Method (MRDM) to Bitstamp 1 min bitcoin returns from January 2013 to July 2020. The results suggest that bitcoin is multifractal, with smaller and larger fluctuations being persistent and anti-persistent, respectively. Multifractality comes from significant long-range correlations, which cast some doubts on the informational efficiency at this frequency, but mainly comes from fat-tails, which highlights the significant risks undertaken by investors in this market. Our most important result...
Journal of Financial Economic Policy, 2019
Purpose This paper aims to examine whether the crypto-currencies’ market returns are symmetric or asymmetric informative, through analysing the daily logarithmic returns of bitcoin currency over the period of 2011-2017. Design/methodology/approach In doing so, the symmetric informative analysis is estimated by applying the generalised auto-regressive conditional heteroscedasticity (GARCH) (1,1) model, whereas asymmetric informative or leverage effects analysis is estimated by exponential GARCH (1,1), asymmetric power ARCH (1,1) and threshold GARCH (1,1) models. In addition, the generalized autoregressive conditional heteroskedasticity in mean (GARCH-M (1,1)) was applied to examine whether the risk-return trade-off phenomenon was persistent in crypto-currencies market. Findings The main findings indicate that bitcoin market return or volatility is symmetric informative and has a long memory to persist in the future. Furthermore, the sympatric volatility is found to be more sensitive ...
The inefficiency of Bitcoin revisited: a dynamic approach
This letter revisits the informational efficiency of the Bitcoin market. In particular we analyze the time-varying behavior of long memory of returns on Bitcoin and volatility 2011 until 2017, using the Hurst exponent. Our results are twofold. First, R/S method is prone to detect long memory , whereas DFA method can discriminate more precisely variations in informational efficiency across time. Second, daily returns exhibit persistent behavior in the first half of the period under study, whereas its behavior is more informational efficient since 2014. Finally, price volatility , measured as the logarithmic difference between intraday high and low prices exhibits long memory during all the period. This reflects a different underlying dynamic process generating the prices and volatility.
On the Market Efficiency and Liquidity of High-Frequency Cryptocurrencies in a Bull and Bear Market
Journal of Risk and Financial Management, 2020
The market for cryptocurrencies has experienced extremely turbulent conditions in recent times, and we can clearly identify strong bull and bear market phenomena over the past year. In this paper, we utilise algorithms for detecting turnings points to identify both bull and bear phases in high-frequency markets for the three largest cryptocurrencies of Bitcoin, Ethereum, and Litecoin. We also examine the market efficiency and liquidity of the selected cryptocurrencies during these periods using high-frequency data. Our findings show that the hourly returns of the three cryptocurrencies during a bull market indicate market efficiency when using the detrended-fluctuation-analysis (DFA) method to analyse the Hurst exponent with a rolling window. However, when conditions turn and there is a bear-market period, we see signs of a more inefficient market. Furthermore, our results indicated differences between the cryptocurrencies in terms of their liquidity during the two market states. Mo...