Abstract This paper evaluates the presence of regime changes in the logâreturns volatility dynamics of cryptocurrencies using MarkovâSwitching GARCH (MSâGARCH) models. The empirical study compares the prediction performance of MSâGARCH against traditional singleâregime GARCH methods for oneâ, fiveâ and tenâstepsâahead volatility forecasting of six leading digital coins such as Bitcoin, Dashcoin, Ethereum, Litecoin, Monero and Ripple. Using a Bayesian approach, different MSâGARCH structures are estimated considering specifications up to three regimes, three scedastic functions and six error distributions, resulting in a total of 54 models for each cryptocurrency. Forecasts are compared according to an economic criterion, that is, through the estimation of ValueâatâRisk (VaR) and Expected Shortfall (ES) risk measures. The results support the evidence of regime changes in the volatility process of selected cryptocurrencies and show that MSâGARCH models do provide more accurate VaR and ES forecasts than their singleâregime counterparts.
The main purpose of our paper is to evaluate the impact of the COVID-19 pandemic on randomness in volatility series of world major markets and to examine its effect on their interconnections. The data set includes equity (Bitcoin and Standard and Poorâs 500), precious metals (Gold and Silver), and energy markets (West Texas Instruments, Brent, and Gas). The generalized autoregressive conditional heteroskedasticity model is applied to the return series. The wavelet packet Shannon entropy is calculated from the estimated volatility series to assess randomness. Hierarchical clustering is employed to examine interconnections between volatilities. We found that (i) randomness in volatility of the S&P500 and in the volatility of precious metals were the most affected by the COVID-19 pandemic, while (ii) randomness in energy markets was less affected by the pandemic than equity and precious metal markets. Additionally, (iii) we showed an apparent emergence of three volatility clusters: precious metals (Gold and Silver), energy (Brent and Gas), and Bitcoin and WTI, and (iv) the S&P500 volatility represents a unique cluster, while (v) the S&P500 market volatility was not connected to the volatility of Bitcoin, energy, and precious metal markets before the pandemic. Moreover, (vi) the S&P500 market volatility became connected to volatility in energy markets and volatility in Bitcoin during the pandemic, and (vii) the volatility in precious metals is less connected to volatility in energy markets and to volatility in Bitcoin market during the pandemic. It is concluded that (i) investors may diversify their portfolios across single constituents of clusters, (ii) investing in energy markets during the pandemic period is appealing because of lower randomness in their respective volatilities, and that (iii) constructing a diversified portfolio would not be challenging as clustering structures are fairly stable across periods.
Chun Kwong Koo, Artur Semeyutin, Chi Keung Marco Lau, Jian Fu
We study the tailsâ behavior of four major Cryptocurrencies (Bitcoin, Litecoin, Ethereum and Ripple) by employing the Autoregressive FrÂŽechet model for conditional maxima. Using five-minute-high-frequency data, we report time-evolving tails as well as provide a straightforward measure of tails asymmetry for positive and negative intra-day returns. We find that only Bitcoin has a notable more massive tail for positive returns asymmetry while the remaining three Cryptocurrencies have a general tendency towards more massive negative intra-day tails. All considered Cryptocurrencies depict lighter tails as the market matures.
Venelina Nikolova, Juan Evangelista Trinidad Segovia, M. FernĂĄndezâMartĂnez, M.A. SĂĄnchez-Granero
One of the main characteristics of cryptocurrencies is the high volatility of their exchange rates. In a previous work, the authors found that a process with volatility clusters displays a volatility series with a high Hurst exponent. In this paper, we provide a novel methodology to calculate the probability of volatility clusters with a special emphasis on cryptocurrencies. With this aim, we calculate the Hurst exponent of a volatility series by means of the FD4 approach. An explicit criterion to computationally determine whether there exist volatility clusters of a fixed size is described. We found that the probabilities of volatility clusters of an index (S&P500) and a stock (Apple) showed a similar profile, whereas the probability of volatility clusters of a forex pair (Euro/USD) became quite lower. On the other hand, a similar profile appeared for Bitcoin/USD, Ethereum/USD, and Ripple/USD cryptocurrencies, with the probabilities of volatility clusters of all such cryptocurrencies being much greater than the ones of the three traditional assets. Our results suggest that the volatility in cryptocurrencies changes faster than in traditional assets, and much faster than in forex pairs.
Huthaifa Alqaralleh, Alaâa Adden Abuhommous, Ahmad Alsaraireh
This study is set out to model and forecast the cryptocurrency market by concentrating on several stylized features of cryptocurrencies. The results of this study assert the presence of an inherently nonlinear mean-reverting process, leading to the presence of asymmetry in the considered return series. Consequently, nonlinear GARCH-type models taking into account distributions of innovations that capture skewness, kurtosis and heavy tails constitute excellent tools for modelling returns in cryptocurrencies. Finally, it is found that, given the high volatility dynamics present in all cryptocurrencies, correct forecasting could help investors to assess the unique risk-return characteristics of a cryptocurrency, thus helping them to allocate their capital.
Abstract Cryptocurrencies are unique and extra-ordinary currencies which to be econometrically forced into the linear model due to their systematic complexity and extreme movements. This paper was conducted to provide an alternative analysis as a solution for escaping the restrictions of traditional linear assumptions. Five predominant digital currencies such as Bitcoin (BTC), Stellar network (XLM), Litecoin (LTC), Ethereum Classic (ETC), and IOTA were chosen to be employed in the multiple processes based on Bayesian approaches. Market dominance and data regime classifications are the essential components that lead to successfully investigate the dependent structures and co-movements in the digital financial market. The empirical findings could assume that the modern time-series data was meticulously estimated by the flexible modern tool. Bayesian statistics and simulations have the sufficient potency as the suitable solution.
Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for inference in pure-jump models. This article shows how to build a simple and precise estimator of the jump activity index of a semimartingale observed at a high frequency by comparing different multipowers. The novel methodology allows to infer whether a discretely observed process contains a continuous martingale component. The empirical part of the article undertakes a nonparametric analysis of the jump activity of bitcoin and shows that bitcoin is a pure jump process with high jump activity, which is critically different from conventional currencies that include a Brownian motion component.
The analysis of cryptocurrencies market behaviour is receiving significant attention from researchers and practitioners in the last decades. This paper aims at contributes to volatility estimations of the cryptocurrencies helping to highlight the main stylized facts and characteristics. The performance of different specifications of volatility modelling, within the GARCH class, have been compared through the Model Confidence Set (MCS) over four of the most capitalised cryptocurrencies, namely Bitcoin, Ethereum, Stellar and Ripple. Our empirical findings give evidence of strong asymmetric effects in cryptocurrencies volatility leading to a better performance of asymmetric GARCH specifications..
In this paper, the pricing performance of the generalised autoregressive conditional heteroskedasticity (GARCH) option pricing model is tested when applied to Bitcoin (BTCUSD). In addition, implied volatility indices (30, 60-and 90-days) of BTCUSD and the Cyptocurrency Index (CRIX) are generated by making use of the symmetric GARCH option pricing model. The results indicate that the GARCH option pricing model produces accurate European option prices when compared to market prices and that the BTCUSD and CRIX implied volatility indices are similar when compared, this is consistent with expectations because BTCUSD is highly weighted when calculating the CRIX. Furthermore, the term structure of volatility indices indicate that short-term volatility (30 days) is generally lower when compared to longer maturities. Furthermore, short-term volatility tends to increase to higher levels when compared to 60 and 90 day volatility when large jumps occur in the underlying asset.
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, ĂzgĂŒr ĂatıkkaĆ, 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 Kupieckâs 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, MĂĄrio 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.