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.
Although Bitcoin has long been dominant in the crypto scene, it is certainly not alone. Ether is another cryptocurrency related project that has attracted an intensive attention because of its additional features. This study seeks to test whether these cryptocurrencies differ in terms of their volatile and speculative behaviors, hedge, safe haven and risk diversification properties. Using different econometric techniques, we show that a) Bitcoin and Ether are volatile and relatively more responsive to bad news, but the volatility of Ether is more persistent than that of Bitcoin; b) for both cryptocurrencies, the exuberance and the collapse of bubbles were identified, but Bitcoin appears more speculative than Ether; c) there is negative and significant correlation between Bitcoin/Ether and other assets (S\&P500 stocks, US bonds, oil), which would indicate that digital currencies can hedge against the price movements of these assets; d) there is negative tail independence between Bitcoin/Ether and other financial assets, implying that these cryptocurrencies exhibit the function of a weak safe haven; and e) The inclusion of Bitcoin/ Ether in a portfolio improve its efficiency in terms of higher reward-to-risk ratios. But investors who hold diversified portfolios made of stocks or bonds and Ether may face losses over bearish regime. In such situation, stock and bond investors may take a short position on Bitcoin.
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.
The long-term dependence of Bitcoin (BTC), manifesting itself through a Hurst\nexponent $H>0.5$, is exploited in order to predict future BTC/USD price. A\nMonte Carlo simulation with $10^4$ geometric fractional Brownian motion\nrealisations is performed as extensions of historical data. The accuracy of\nstatistical inferences is 10\\%. The most probable Bitcoin price at the\nbeginning of 2018 is 6358 USD.\n
This article demonstrates the possibility of constructing indicators of critical and crisis phenomena in the volatile market of cryptocurrency. For this purpose, the methods of the theory of complex systems such as recurrent analysis of dynamic systems and the calculation of permutation entropy are used. It is shown that it is possible to construct dynamic measures of complexity, both recurrent and entropy, which behave in a proper way during actual pre-crisis periods. This fact is used to build predictors of crisis phenomena on the example of the main five crises recorded in the time series of the key cryptocurrency bitcoin, the effectiveness of the proposed indicators-precursors of crises has been identified.
Aurelio F. Bariviera, María José Basgall, Waldo Hasperué, Marcelo Naiouf
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.
The growth of peer-to-peer exchanges and the blockchain technology has led to a proliferation of cryptocurrencies and to a massive increase in the number of investors who actually negotiate digital money. Cryptocurrencies trade at prices mainly driven by investor sentiment, becoming a potential source of financial bubbles and instabilities. In this work, we apply quantitative models to the study of Bitcoin and Ether, two of the most famous cryptocurrencies. Our bubble detection methodology combines the Log Periodic Power Law (LPPL) model, originally created by Johansen, Ledoit and Sornette (JLS), and the statistical model developed by Phillips, Shi, and Yu (PSY). In particular, we employ three different versions of JLS model, i.e. Ordinary Least Square (OLS), Generalised Least Squares (GLS) and Maximum Likelihood Estimation (MLE), and two PSY statistical tests (BSADF and BSADF*). We find that, during the sample period 1st December 2016 - 16th January 2018, Bitcoin shows typical hallmarks of a bubble phase in mid December 2017 and in the first half of January 2018, anticipating the large crashes observed thereafter. Also the Ether price dynamics reveals bubble evidence in mid June 2017, anticipating the crash observed on 12th June, and a weaker signal around 12th January 2018, anticipating the crash observed in the same days. This paper confirms the high risk of speculative bubbles associated with cryptocurrencies, related to investor exuberance pumping market prices far away from their fundamental values, thus creating critical situations subject to possible crashes. Our methodology is general and can be applied to virtually any financial time series, and may support investing and risk management strategies.
Attempts to accurately measure the monetary velocity or related properties of Bitcoin have often attempted to either directly apply definitions from traditional macroeconomic theory or to use specialized metrics relative to the properties of the Blockchain such as bitcoin-days destroyed. In this paper, it is demonstrated that beyond being a useful metric, bitcoin-days destroyed has mathematical properties that allow one to calculate the average dormancy (time since last use in a transaction) of the bitcoins used in transactions over a given time period. In addition, transaction volume and average dormancy are shown to have unexpected significance in helping estimate the average size of the pool of traded bitcoins by virtue of the expression Little's Law, though only under limited conditions.
Olivier Scaillet, Adrien Treccani, Christopher Trevisan
We use the database leak of Mt. Gox exchange to analyze the dynamics of the price of bitcoin from June 2011 to November 2013. This gives us a rare opportunity to study an emerging retail-focused, highly speculative and unregulated market with trader identifiers at a tick transaction level. Jumps are frequent events and they cluster in time. The order flow imbalance and the preponderance of aggressive traders, as well as a widening of the bid-ask spread predict them. Jumps have short-term positive impact on market activity and illiquidity and induce a persistent change in the price.
We show that the behaviour of Bitcoin has interesting similarities to stock\nand precious metal markets, such as gold and silver. We report that whilst\nLitecoin, the second largest cryptocurrency, closely follows Bitcoin's\nbehaviour, it does not show all the reported properties of Bitcoin. Agreements\nbetween apparently disparate complexity measures have been found, and it is\nshown that statistical, information-theoretic, algorithmic and fractal measures\nhave different but interesting capabilities of clustering families of markets\nby type. The report is particularly interesting because of the range and novel\nuse of some measures of complexity to characterize price behaviour, because of\nthe IRS designation of Bitcoin as an investment property and not a currency,\nand the announcement of the Canadian government's own electronic currency\nMintChip.\n
David García, Claudio J. Tessone, Pavlin Mavrodiev, Nicolas Perony
What is the role of social interactions in the creation of price bubbles? Answering this question requires obtaining collective behavioural traces generated by the activity of a large number of actors. Digital currencies offer a unique possibility to measure socio-economic signals from such digital traces. Here, we focus on Bitcoin, the most popular cryptocurrency. Bitcoin has experienced periods of rapid increase in exchange rates (price) followed by sharp decline; we hypothesise that these fluctuations are largely driven by the interplay between different social phenomena. We thus quantify four socio-economic signals about Bitcoin from large data sets: price on on-line exchanges, volume of word-of-mouth communication in on-line social media, volume of information search, and user base growth. By using vector autoregression, we identify two positive feedback loops that lead to price bubbles in the absence of exogenous stimuli: one driven by word of mouth, and the other by new Bitcoin adopters. We also observe that spikes in information search, presumably linked to external events, precede drastic price declines. Understanding the interplay between the socio-economic signals we measured can lead to applications beyond cryptocurrencies to other phenomena which leave digital footprints, such as on-line social network usage.
The Bitcoin has emerged as a fascinating phenomenon in the Financial markets. Without any central authority issuing the currency, the Bitcoin has been associated with controversy ever since its popularity, accompanied by increased public interest, reached high levels. Here, we contribute to the discussion by examining the potential drivers of Bitcoin prices, ranging from fundamental sources to speculative and technical ones, and we further study the potential influence of the Chinese market. The evolution of relationships is examined in both time and frequency domains utilizing the continuous wavelets framework, so that we not only comment on the development of the interconnections in time but also distinguish between short-term and long-term connections. We find that the Bitcoin forms a unique asset possessing properties of both a standard financial asset and a speculative one.