In this study, we investigate the existence of chaos in the global cryptocurrency market. Specifically, we analyze parameters of chaotic order, nonlinearity, sensitivity to the initial conditions, monofractality, and multifractality. For this purpose, we conduct a comprehensive series of tests, including Brock–Dechert–Scheinkman (BDS) test, largest Lyapunov exponent, box-counting, and monogram analysis for fractal dimension, and multiple tests for long-range dependence (Aggregated Variances, Peng, Higuchi, R/S Analysis, and Multifractal Detrended Fluctuation Analysis (MFDFA)). All tests are performed over a variety of major cryptocurrencies: Bitcoin, Litecoin, Ethereum, and Ripple. The empirical results support the existence of chaos in the cryptocurrency market. Accordingly, cryptocurrency returns are not random and follow a chaotic order. Therefore, long term predictions are not possible, contrary to most of the discussions ongoing in the media and the public.
José Antonio Núñez Mora, Mario Iván Contreras-Valdez, Carlos A. Franco-Ruiz
This paper develops the ability of the normal inverse Gaussian distribution (NIG) to fit the returns of bitcoin (BTC). As the first cryptocurrency created, the behavior of this new asset is characterized by great volatility. The lack of a proper definition or classification under existing theory exacerbates this property in such a way that explosive periods followed by a rapid decline have been observed along the series, meaning bubble episodes. By detecting the periods in which a bubble rises and collapses, it is possible to study the statistical properties of such segments. In particular, adjusting a theoretical distribution may help to determine better strategies to hedge against these episodes. The NIG is an appropriate candidate not only because of its heavy-tailed property but also because it has been proven to be closed under convolution, a characteristic that can be implemented to measure multivariate value at risk. Using data on the price of BTC with respect to seven of the main global currencies, the NIG was able to fit every time segment despite the bubble behavior. In the out-of-sample tests, the NIG was proven to have an adjustment similar to that of a generalized hyperbolic (GH) distribution. This result could serve as a starting point for future studies regarding the statistical properties of cryptocurrencies as well as their multivariate distributions.
<p>This paper is aimed at studying a MS-GARCH model applied to Bitcoin. The Bayesian estimation of the model shows that Bitcoin’s volatility can be modelled using two states of volatility, high and low. The modelled volatility is not stable over time. Twenty eight periods of high volatility were found, the largest period of volatility occurred during 2013. The findings help explain what happened during these high volatility periods.</p><p> </p><p><strong> </strong></p>
Abstract Using extreme value analysis, we investigate the tail risk behavior of the high‐frequency (hourly) log returns of four most popular cryptocurrencies. The analysis is conducted on high‐frequency returns data, estimating value at risk and expected shortfall with varying thresholds. We find that Ripple is the most risky cryptocurrency exhibiting the largest potential gain or loss for both positive and negative (hourly) log returns at every percentile and threshold. Bitcoin is the least risky cryptocurrency.
Daniel Traian Pele, Miruna Mazurencu-Marinescu-Pele
In this paper we investigate the ability of several econometrical models to forecast value at risk for a sample of daily time series of cryptocurrency returns. Using high frequency data for Bitcoin, we estimate the entropy of intraday distribution of logreturns through the symbolic time series analysis (STSA), producing low-resolution data from high-resolution data. Our results show that entropy has a strong explanatory power for the quantiles of the distribution of the daily returns. Based on Christoffersen's tests for Value at Risk (VaR) backtesting, we can conclude that the VaR forecast build upon the entropy of intraday returns is the best, compared to the forecasts provided by the classical GARCH models.
Higor Y. D. Sigaki, Matjaž Perc, Haroldo V. Ribeiro
The efficient market hypothesis has far-reaching implications for financial trading and market stability. Whether or not cryptocurrencies are informationally efficient has therefore been the subject of intense recent investigation. Here, we use permutation entropy and statistical complexity over sliding time-windows of price log returns to quantify the dynamic efficiency of more than four hundred cryptocurrencies. We consider that a cryptocurrency is efficient within a time-window when these two complexity measures are statistically indistinguishable from their values obtained on randomly shuffled data. We find that 37% of the cryptocurrencies in our study stay efficient over 80% of the time, whereas 20% are informationally efficient in less than 20% of the time. Our results also show that the efficiency is not correlated with the market capitalization of the cryptocurrencies. A dynamic analysis of informational efficiency over time reveals clustering patterns in which different cryptocurrencies with similar temporal patterns form four clusters, and moreover, younger currencies in each group appear poised to follow the trend of their 'elders'. The cryptocurrency market thus already shows notable adherence to the efficient market hypothesis, although data also reveals that the coming-of-age of digital currencies is in this regard still very much underway.
In this paper, we revisit the stylized facts of cryptocurrency markets and propose various approaches for modeling the dynamics governing the mean and variance processes. We first provide the statistical properties of our proposed models and study in detail their forecasting performance and adequacy by means of point and density forecasts. We adopt two loss functions and the model confidence set (MSC) test to evaluate the predictive ability of the models and the likelihood ratio test to assess their adequacy. Our results confirm that cryptocurrency markets are characterized by regime shifting, long memory and multifractality. We find that the Markov switching multifractal (MSM) and FIGARCH models outperform other GARCH-type models in forecasting bitcoin returns volatility. Furthermore, combined forecasts improve upon forecasts from individual models.
Anwar Hasan Abdullah Othman, Syed Musa Alhabshi, Razali Haron
This study investigates whether symmetric and asymmetric volatility effects are persisted in the daily return series of Bitcoin currency compared to the gold and fiat money system using GARCH family models. The symmetric analysis shows that the three monetary systems exhibit time-varying volatility with high persistence and predictability behaviour whereas asymmetric analysis indicates that Bitcoin currency and gold are not significantly respond to asymmetric information effects in the financial markets however, the US dollar index is affected by the positive shocks. This suggesting Bitcoin and gold have the capability for hedging or safe-haven assets against market risk specifically during times of economic turmoil. Evidence suggests that cryptocurrency is a potential alternative to current fiat money system, offering benefit for policy makers and a good investment option for positional investors in terms of hedging, portfolio diversification strategy and risk management.
Cryptocurrency, the most controversial and simultaneously the most interesting asset, has attracted many investors and speculators in recent years. The visibly significant market capitalization of cryptos also motivates modern financial instruments such as futures and options. Those will depend on the dynamics, volatility, or even the jumps of cryptos. We provide a comprehensive investigation of the risk dynamics of the Bitcoin Market from a realized volatility perspective. The Bitcoin market is extremely risky in the sense of volatility, entangled jumps, and extensive consecutive jumps, which reflect the major incidents worldwide. Empirical study shows that the lagged realized variance increases the future realized variance, while the jumps, especially positive ones, significantly reduce future realized variance. The out-of-sample forecasting model reveals that, in terms of forecasting accuracy and utility gain, investors interested in the long-term realized variance benefit from explicitly modelling the jumps and signed estimators, which is unnecessary for the short-term realized variance forecast.
In this paper we study the daily volatility of four cryptocurrencies (BitCoin, Dash, LiteCoin, and Ripple) from June 2014 to November 2018. We first show that the cryptocurrency returns are strongly characterized by the presence of jumps as well as structural breaks (except Dash). Then, we estimate four GARCH-type models that capture short memory (GARCH), asymmetry (APARCH), strong persistence (IGARCH), and long memory (FIGARCH) from (i) original returns, (ii) jump-filtered returns, and (iii) jump-filtered returns with structural breaks. Results indicate the importance to take into account the jumps and structural breaks in modelling volatility of the cryptocurrencies. It appears that the cryptocurrency returns are well modelled by infinite persistence (BitCoin, Dash, and LiteCoin) or long memory (Ripple) with a Student-t distribution.