Volatility estimation for Bitcoin: A comparison of GARCH models

We explore the optimal conditional heteroskedasticity model with regards to goodness-of-fit to Bitcoin price data. It is found that the best model is the AR-CGARCH model, highlighting the significance of including both a short-run and a long-run component of the conditional variance

A new approach to modelling nonlinear time series: introducing the ExpAR-ARCH and ExpAR-GARCH models and applications

The analysis of time series has long been the subject of interest in different fields. For decades time series were analysed with linear models. Nevertheless, an issue that has been raised is whether there exist other models that can explain and fit real data better than linear ones. In this paper, new nonlinear time series models are proposed (namely the ExpAR-ARCH and the ExpAR-GARCH), which are combinations of a nonlinear model in the conditional mean and a nonlinear model in the conditional variance and have the potential of explaining observed data in various fields. Simulated data of these models are presented, while different algorithms (the Nelder-Mead simplex direct search method, the Quasi-Newton line search algorithm, the Active-Set algorithm, the Sequential Quadratic Programming algorithm, the Interior Point algorithm and a Genetic Algorithm) are used and compared in order to check their estimation performance when it comes to these suggested nonlinear models. Moreover, an application to the Dow Jones data is considered, showing that the new models can explain real data better than the AR-ARCH and AR-GARCH models. © Paraskevi Katsiampa

Nonlinear exponential autoregressive time series models with conditional heteroskedastic errors with applications to economics and finance

The analysis of time series has long been the subject of interest in different fields. For decades time series were analysed with linear models, which have many advantages. Nevertheless, an issue which has been raised is whether there exist other models that can explain and forecast real data better than linear ones. In this thesis, new nonlinear time series models are suggested, which consist of a nonlinear conditional mean model, such as an ExpAR or an Extended ExpAR, and a nonlinear conditional variance model, such as an ARCH or a GARCH. Since new models are introduced, simulated series of the new models are presented, as it is important in order to see what characteristics real data which could be explained by them should have. In addition, the models are applied to various stationary and nonstationary economic and financial time series and are compared to the classic AR-ARCH and AR-GARCH models, in terms of fitting and forecasting. It is shown that, although it is difficult to beat the AR-ARCH and AR-GARCH models, the ExpAR and Extended ExpAR models and their special cases, combined with conditional heteroscedastic errors, can be useful tools in fitting, describing and forecasting nonlinear behaviour in financial and economic time series, and can provide some improvement in terms of both fitting and forecasting compared to the AR-ARCH and AR-GARCH models

An application of extreme value theory to cryptocurrencies

We study the tail behaviour of the returns of five major cryptocurrencies. By employing an extreme value analysis and estimating Value-at-Risk and Expected Shortfall as tail risk measures, we find that Bitcoin Cash is the riskiest, while Bitcoin and Litecoin are the least risky cryptocurrencies

Asymmetric mean reversion of Bitcoin price returns

© 2018 Elsevier Inc. Non-linearity is characterised by an asymmetric mean-reverting property, which has been found to be inherent in the short-term return dynamics of stocks. In this paper, we explore as to whether cryptocurrency returns, as represented by Bitcoin, exhibit similar asymmetric reverting patterns for minutely, hourly, daily and weekly returns between June 2010 and February 2018. We identify several differences in the behaviour of Bitcoin price returns in the pre- and post-$1000 sub-periods and evidence of asymmetric reverting patterns in the Bitcoin price returns under all the ANAR models employed, regardless of the data frequency considered. We also present evidence indicating stronger reverting behaviour of negative price returns in terms of both reverting speed and magnitude compared to positive returns and evidence of positive serial correlation with prior positive price returns. Finally, we also investigated asymmetries in Bitcoin price return series’ persistence by employing higher order ANAR models, finding evidence of a higher persistence of positive returns than negative returns, a result that further supports the existence of asymmetric reverting behaviour in the Bitcoin price returns

Discontinuous movements and asymmetries in cryptocurrency markets

This paper proposes a novel asymmetric jump model for modeling interactions in discontinuous movements in asset prices. Given the jump behavior and high volatility levels in cryptocurrency markets, we apply our model to cryptocurrencies to study the impact of various types of jumps occurring in one cryptocurrency’s price process on the discontinuity component of the realized volatility of other cryptocurrencies. Our model also allows us to assess the impact of co-jumps. Using high-frequency data to compute the daily realized volatility, we show that downside, upside, and small jumps observed in cryptocurrencies negatively affect the jump component of other cryptocurrencies’ realized volatility, while large jumps have the opposite effect. We further find significant asymmetric effects between small and large as well as between downside and upside jumps for several cryptocurrencies. Moreover, we find evidence of co-jumping behavior, which can trigger future jumps. The practical implications of our findings are also discussed. Finally, we extend our analysis to study the effects of jumps in mainstream financial assets on cryptocurrencies’ jump behavior and find that upside and downside jumps observed in the S&P 500 index negatively impact cryptocurrency jumps

An application of extreme value theory to cryptocurrencies

We study the tail behaviour of the returns of five major cryptocurrencies. By employing an extreme value analysis and estimating Value-at-Risk and Expected Shortfall as tail risk measures, we find that Bitcoin Cash is the riskiest, while Bitcoin and Litecoin are the least risky cryptocurrencies

Volatility co-movement between Bitcoin and Ether

Using a bivariate Diagonal BEKK model, this paper investigates the volatility dynamics of the two major cryptocurrencies, namely Bitcoin and Ether. We find evidence of interdependencies in the cryptocurrency market, while it is shown that the two cryptocurrencies' conditional volatility and correlation are responsive to major news. In addition, we show that Ether can be an effective hedge against Bitcoin, while the analysis of optimal portfolio weights indicates that Bitcoin should outweigh Ether. Understanding volatility movements and interdependencies in cryptocurrency markets is important for appropriate investment management, and our study can thus assist cryptocurrency users in making more informed decisions

High frequency volatility co-movements in cryptocurrency markets

Through the application of Diagonal BEKK and Asymmetric Diagonal BEKK methodologies to intra-day data for eight cryptocurrencies, this paper investigates not only conditional volatility dynamics of major cryptocurrencies, but also their volatility co-movements. We first provide evidence that all conditional variances are significantly affected by both previous squared errors and past conditional volatility. It is also shown that both methodologies indicate that cryptocurrency investors pay the most attention to news relating to Neo and the least attention to news relating to Dash, while shocks in OmiseGo persist the least and shocks in Bitcoin persist the most, although all of the considered cryptocurrencies possess high levels of persistence of volatility over time. We also demonstrate that the conditional covariances are significantly affected by both cross-products of past error terms and past conditional covariances, suggesting strong interdependencies between cryptocurrencies. It is also demonstrated that the Asymmetric Diagonal BEKK model is a superior choice of methodology, with our results suggesting significant asymmetric effects of positive and negative shocks in the conditional volatility of the price returns of all of our investigated cryptocurrencies, while the conditional covariances capture asymmetric effects of good and bad news accordingly. Finally, it is shown that time-varying conditional correlations exist, with our selected cryptocurrencies being strongly positively correlated, further highlighting interdependencies within cryptocurrency markets

An empirical investigation of volatility dynamics in the cryptocurrency market

By employing an asymmetric Diagonal BEKK model, this paper examines volatility dynamics of five major cryptocurrencies, namely Bitcoin, Ether, Ripple, Litecoin, and Stellar Lumen. It is shown that the conditional variances of all the five cryptocurrencies are significantly affected by both previous squared errors and past conditional volatility. Moreover, in the case of Bitcoin, Ether, Ripple, and Litecoin, asymmetric past shocks have a significant effect in the current conditional variance. Similar results are obtained for the cryptocurrencies' conditional covariances, which are significantly affected by cross products of previous error terms and past covariance terms while capturing asymmetric effects of past shocks accordingly. It is also shown that time-varying conditional correlations exist and are mostly positive. Finally, the cryptocurrencies' volatility dynamics are found to be responsive to major news, with Bitcoin and Litecoin exhibiting one structural breakpoint each in the conditional variance. The results improve our understanding of interdependencies between cryptocurrencies as well as of the events that affect their volatility dynamics and thus have important implications for both cryptocurrency users and investors