Bitcoin volatility was investigated with various symmetric and asymmetric models in the study. In addition, value at risk (VaR) was calculated by using the Kupiec LR test and the error prediction performances of the models were compared. As a result of the work, the long memory of volatility in Bitcoin returns was found. It means the cryptocurrency market is not efficient. According to the FIAPARCH asymmetric model, it was determined that positive information shocks reaching the Bitcoin market increased volatility more than negative information shocks. Comparing the error prediction performance of the models by calculating VaR, the HYGARCH model prediction results were found to be superior to other models included in the study. Thus, it was determined that the most suitable model in predicting the volatility, namely the risk of Bitcoin in short and long positions for those who consider investing in Bitcoin, is the asymmetric model HYGARCH.
This paper examines the behaviour of Bitcoin returns and those of several other cryptocurrencies in the pre and post period of the introduction of the Bitcoin futures market. We use the principal component-guided sparse regression (PC-LASSO) model to analyze several sample sizes for the pre and post periods. Besides the neighbourhood of the break time, the current period is also investigated as returns start to recover after some time. Search intensity is observed to be the most important variable for Bitcoin for all periods, whereas for the other cryptocurrencies there are other variables that seem more important in the pre period, while search intensity still stands out in the post period. Furthermore, GARCH analyses suggest that search intensity increases the volatility of Bitcoin returns more in the post period than it does in the pre period. Our empirical findings suggest that the top five cryptocurrencies are substitutes before the launch of Bitcoin futures. However, this effect is lost, and moreover, there are spillover effects on altcoins during both the post and the recovery period. We find a spillover effect of the introduction of bitcoin futures on altcoins and this effect seems to persist during the recovery period.
Pınar Kaya Soylu, Mustafa Okur, Özgür Çatıkkaş, Ayca Altintig
This paper examines the volatility of cryptocurrencies, with particular attention to their potential long memory properties. Using daily data for the three major cryptocurrencies, namely Ripple, Ethereum, and Bitcoin, we test for the long memory property using, Rescaled Range Statistics (R/S), Gaussian Semi Parametric (GSP) and the Geweke and Porter-Hudak (GPH) Model Method. Our findings show that squared returns of three cryptocurrencies have a significant long memory, supporting the use of fractional Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) extensions as suitable modelling technique. Our findings indicate that the Hyperbolic GARCH (HYGARCH) model appears to be the best fitted model for Bitcoin. On the other hand, the Fractional Integrated GARCH (FIGARCH) model with skewed student distribution produces better estimations for Ethereum. Finally, FIGARCH model with student distribution appears to give a good fit for Ripple return. Based on Kupieck’s tests for Value at Risk (VaR) back-testing and expected shortfalls we can conclude that our models perform correctly in most of the cases for both the negative and positive returns.
Multifractal processes reproduce some of the stylised features observed in financial time series, namely heavy tails found in asset returns distributions, and long-memory found in volatility. Multifractal scaling cannot be assumed, it should be established; however, this is not a straightforward task, particularly in the presence of heavy tails. We develop an empirical hypothesis test to identify whether a time series is likely to exhibit multifractal scaling in the presence of heavy tails. The test is constructed by comparing estimated scaling functions of financial time series to simulated scaling functions of both an iid Student t-distributed process and a Brownian Motion in Multifractal Time (BMMT), a multifractal processes constructed in Mandelbrot et al. (1997). Concavity measures of the respective scaling functions are estimated, and it is observed that the concavity measures form different distributions which allow us to construct a hypothesis test. We apply this method to test for multifractal scaling across several financial time series including Bitcoin. We observe that multifractal scaling cannot be ruled out for Bitcoin or the Nasdaq Composite Index, both technology driven assets.
We study the problem of the intraday short-term volume forecasting in cryptocurrency exchange markets. The predictions are built by using transaction and order book data from different markets where the exchange takes place. Methodologically, we propose a temporal mixture ensemble, capable of adaptively exploiting, for the forecasting, different sources of data and providing a volume point estimate, as well as its uncertainty. We provide evidence of the outperformance of our model by comparing its outcomes with those obtained with different time series and machine learning methods. Finally, we discuss the predictions conditional to volume and we find that also in this case machine learning methods outperform econometric models.
Roy Cerqueti, Massimiliano Giacalone, Raffaele Mattera
Recently, cryptocurrencies have attracted a growing interest from investors,\npractitioners and researchers. Nevertheless, few studies have focused on the\npredictability of them. In this paper we propose a new and comprehensive study\nabout cryptocurrency market, evaluating the forecasting performance for three\nof the most important cryptocurrencies (Bitcoin, Ethereum and Litecoin) in\nterms of market capitalization. At this aim, we consider non-Gaussian GARCH\nvolatility models, which form a class of stochastic recursive systems commonly\nadopted for financial predictions. Results show that the best specification and\nforecasting accuracy are achieved under the Skewed Generalized Error\nDistribution when Bitcoin/USD and Litecoin/USD exchange rates are considered,\nwhile the best performances are obtained for skewed Distribution in the case of\nEthereum/USD exchange rate. The obtain findings state the effectiveness -- in\nterms of prediction performance -- of relaxing the normality assumption and\nconsidering skewed distributions.\n
Roy Cerqueti, Massimiliano Giacalone, Raffaele Mattera
Recently, cryptocurrencies have attracted a growing interest from investors, practitioners and researchers. Nevertheless, few studies have focused on the predictability of them. In this paper we propose a new and comprehensive study about cryptocurrency market, evaluating the forecasting performance for three of the most important cryptocurrencies (Bitcoin, Ethereum and Litecoin) in terms of market capitalization. At this aim, we consider non-Gaussian GARCH volatility models, which form a class of stochastic recursive systems commonly adopted for financial predictions. Results show that the best specification and forecasting accuracy are achieved under the Skewed Generalized Error Distribution when Bitcoin/USD and Litecoin/USD exchange rates are considered, while the best performances are obtained for skewed Distribution in the case of Ethereum/USD exchange rate. The obtain findings state the effectiveness -- in terms of prediction performance -- of relaxing the normality assumption and considering skewed distributions.
In this paper, we analyze the time-series of minute price returns on the Bitcoin market through the statistical models of generalized autoregressive conditional heteroskedasticity (GARCH) family. Several mathematical models have been proposed in finance, to model the dynamics of price returns, each of them introducing a different perspective on the problem, but none without shortcomings. We combine an approach that uses historical values of returns and their volatilities - GARCH family of models, with a so-called "Mixture of Distribution Hypothesis", which states that the dynamics of price returns are governed by the information flow about the market. Using time-series of Bitcoin-related tweets and volume of transactions as external information, we test for improvement in volatility prediction of several GARCH model variants on a minute level Bitcoin price time series. Statistical tests show that the simplest GARCH(1,1) reacts the best to the addition of external signal to model volatility process on out-of-sample data.
F. N. M. de Sousa Filho, J. N. Silva, Mário Augusto Bertella, Edgardo Brigatti
In this paper, we explore some stylized facts in the Bitcoin market using the BTC-USD exchange rate time series of historical intraday data from 2013 to 2018. Despite Bitcoin presents some very peculiar idiosyncrasies, like the absence of macroeconomic fundamentals or connections with underlying asset or benchmark, a clear asymmetry between demand and supply and the presence of inefficiency in the form of very strong arbitrage opportunity, all these elements seem to be marginal in the definition of the structural statistical properties of this virtual financial asset, which result to be analogous to general individual stocks or indices. In contrast, we find some clear differences, compared to fiat money exchange rates time series, in the values of the linear autocorrelation and, more surprisingly, in the presence of the leverage effect. We also explore the dynamics of correlations, monitoring the shifts in the evolution of the Bitcoin market. This analysis is able to distinguish between two different regimes: a stochastic process with weaker memory signatures and closer to Gaussianity between the Mt. Gox incident and the late 2015, and a dynamics with relevant correlations and strong deviations from Gaussianity before and after this interval.
This paper aims at identifying a validated risk model for the cryptocurrency market. We propose a stochastic volatility model with co-jumps in return and volatility (SVCJ) to highlight the role of jumps in returns and volatility in affecting Value-at-Risk (VaR) and Expected Shortfall (ES) in cryptocurrency market. Validation results based on backtesting show that SVCJ model is superior in terms of statistical accuracy of VaR and ES estimates, compared to alternative models such as TGARCH (Threshold GARCH) volatility and RiskMetrics models. The results imply that for the cryptocurrency market, the best performing model is a stochastic process that accounts for both jumps in returns and volatility.
This paper compares a number of stochastic volatility (SV) models for modeling and predicting the volatility of the four most capitalized cryptocurrencies (Bitcoin, Ethereum, Ripple, and Litecoin). The standard SV model, models with heavy-tails and moving average innovations, models with jumps, leverage effects and volatility in mean were considered. The Bayes factor for model fit was largely in favor of the heavy-tailed SV model. The forecasting performance of this model was also found superior than the other competing models. Overall, the findings of this study suggest using the heavy-tailed stochastic volatility model for modeling and forecasting the volatility of cryptocurrencies.
This paper studies of the multifractal dynamics in 84 cryptocurrencies. It fills an important gap in the literature, by studying this market using two alternative multi-scaling methodologies. We find compelling evidence that cryptocurrencies have different degree of long range dependence, and --more importantly -- follow different stochastic processes. Some of them follow models closer to monofractal fractional Gaussian noises, while others exhibit complex multifractal dynamics. Regarding the source of multifractality, our results are mixed. Time series shuffling produces a reduction in the level of multifractality, but not enough to offset it. We find an association of kurtosis with multifractality.
This letter expands the studies of the informational efficiency in the cryptocurrency market. Most studies have focused on Bitcoin, the foremost known cryptocurrency, and a few more coins. However, this market is more diverse, with cryptocurrencies entering and leaving the market on a weekly basis. This letter fills an important gap in the literature, by studying the informational efficiency using a multi-scaling methodology, which represents a new approach. We compute the generalized Hurst exponent of eighty-four cryptoassets daily returns. The multi-scaling methodology used in this paper find compelling evidence that cryptocurrencies have different degree of long range dependence, and --more importantly -- follow different stochastic processes. Some of them follow traditional monofractal models consistent with fractional Brownian motion, while others exhibit complex multifractal dynamics.
This paper examines the volatility spillovers between Bitcoin market and US banking industry using unrestricted BEKK-GARCH model. The results show that there is a strong short-term volatility spillover effect in the two markets. However, Bitcoin trading volatility process weakens the short-term volatility spillover effect from Bitcoin market to banking industry in the United States and the volatility of banking industry returns (i.e. volatility of operational results) weakens the short-term volatility spillover effect from banking industry to Bitcoin market mainly due to inability of adoption in the short-run. Moreover, there is a significant and (positive) long-term volatility spillover effect from Bitcoin market to banking industry. This remarkable observation reveals that there is a possibility of banking industry adopting Bitcoin operation as a part of banking product portfolio development in the long-run. As such, imposition of any tax or trading restriction (e.g. price bands, transaction cost, tax etc.) on Bitcoin market will adversely impact the performance of banking industry in the long-run. The nature of the impact and its timing are of utmost importance for the government and policymakers, particularly in case of economic planning and restructuring of banking and financial services industry.
In recent years cryptocurrency trading has captured the attention of practitioners and academics. The volume of the exchange with standard currencies has known a dramatic increasing of late. This paper addresses to the need of models describing a bitcoin-US dollar exchange dynamic and their use to evaluate European option having bitcoin as underlying asset.