Forecasting Bitcoin risk measures: A robust approach

Abstract Over the last few years, Bitcoin and other cryptocurrencies have attracted the interest of many investors, practitioners and researchers. However, little attention has been paid to the predictability of their risk measures. This paper compares the predictability of the one-step-ahead volatility and Value-at-Risk of Bitcoin using several volatility models. We also include procedures that take into account the presence of outliers and estimate the volatility and Value-at-Risk in a robust fashion. Our results show that robust procedures outperform non-robust ones when forecasting the volatility and estimating the Value-at-Risk. These results suggest that the presence of outliers plays an important role in the modelling and forecasting of Bitcoin risk measures.

[1]  A. Grané,et al.  Additive Level Outliers in Multivariate GARCH Models , 2014 .

[2]  H. Iemoto.  Modelling the persistence of conditional variances , 1986 .

[3]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[4]  Andrew Harvey,et al.  Beta-t-(E)GARCH , 2008 .

[5]  Paraskevi Katsiampa.  Volatility estimation for Bitcoin: A comparison of GARCH models , 2017 .

[6]  Elie Bouri,et al.  Can Volume Predict Bitcoin Returns and Volatility? A Quantiles-Based Approach , 2017 .

[7]  Kris Boudt,et al.  Robust Forecasting of Dynamic Conditional Correlation GARCH Models , 2012 .

[8]  Eric Ghysels,et al.  Stock Market Volatility and Macroeconomic Fundamentals , 2013, Review of Economics and Statistics.

[9]  Viviane Y. Naimy,et al.  Modelling and predicting the Bitcoin volatility using GARCH models , 2018, Int. J. Math. Model. Numer. Optimisation.

[10]  Siem Jan Koopman,et al.  Forecasting Daily Variability of the S&P 100 Stock Index Using Historical, Realised and Implied Volatility Measurements , 2005 .

[11]  J. Zakoian.  Threshold heteroskedastic models , 1994 .

[12]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[13]  Genaro Sucarrat,et al.  EGARCH models with fat tails, skewness and leverage , 2014, Comput. Stat. Data Anal..

[14]  F. Blasques,et al.  Maximum Likelihood Estimation for Generalized Autoregressive Score Models , 2014 .

[15]  Franz C. Palm,et al.  Testing for jumps in conditionally Gaussian ARMA-GARCH models, a robust approach , 2016, Comput. Stat. Data Anal..

[16]  Leopoldo Catania,et al.  Predicting the Volatility of Cryptocurrency Time–Series , 2018 .

[17]  Amélie Charles,et al.  Volatility estimation for Bitcoin: Replication and robustness , 2019, International Economics.

[18]  A. H. Dyhrberg.  Bitcoin, gold and the dollar – A GARCH volatility analysis , 2016 .

[19]  Yaohao Peng,et al.  The best of two worlds: Forecasting high frequency volatility for cryptocurrencies and traditional currencies with Support Vector Regression , 2018, Expert Syst. Appl..

[20]  F. Diebold,et al.  Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility , 2005, The Review of Economics and Statistics.

[21]  V. Cermak.  Can Bitcoin Become a Viable Alternative to Fiat Currencies? An Empirical Analysis of Bitcoin's Volatility Based on a GARCH Model , 2017 .

[22]  Christophe Croux,et al.  Robust exponential smoothing of multivariate time series , 2010, Comput. Stat. Data Anal..

[23]  T. Walther,et al.  Exogenous Drivers of Bitcoin and Cryptocurrency Volatility – A Mixed Data Sampling Approach to Forecasting , 2018, Journal of International Financial Markets, Institutions and Money.

[24]  Christian Conrad,et al.  Long- and Short-Term Cryptocurrency Volatility Components: A GARCH-MIDAS Analysis , 2018 .

[25]  Taisei Kaizoji,et al.  Volatility Analysis of Bitcoin Price Time Series , 2017 .

[26]  Kevin Sheppard,et al.  Does Anything Beat 5-Minute RV? A Comparison of Realized Measures Across Multiple Asset Classes , 2012 .

[27]  F. Iqbal.  Robust Estimation for the Orthogonal GARCH Model , 2012 .

[28]  Luiz Koodi Hotta,et al.  Inference in (M)GARCH Models in the Presence of Additive Outliers: Specification, Estimation, and Prediction , 2018 .

[29]  N. Shephard,et al.  Power and bipower variation with stochastic volatility and jumps , 2003 .

[30]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[31]  Aviral Kumar Tiwari,et al.  Bitcoin returns and risk: A general GARCH and GAS analysis , 2019, Finance Research Letters.

[32]  Peter F. Christoffersen.  Evaluating Interval Forecasts , 1998 .

[33]  Pedro Correia S. Bezerra,et al.  Volatility forecasting via SVR–GARCH with mixture of Gaussian kernels , 2017, Comput. Manag. Sci..

[34]  A. Szafarz,et al.  Virtual currency, tangible return: Portfolio diversification with bitcoin , 2015 .

[35]  Ernst Schaumburg,et al.  Federal Reserve Bank of New York Staff Reports Jump-robust Volatility Estimation Using Nearest Neighbor Truncation Jump-robust Volatility Estimation Using Nearest Neighbor Truncation , 2010 .

[36]  Szabolcs Blazsek,et al.  Is Beta-t-EGARCH(1,1) superior to GARCH(1,1)? , 2015 .

[37]  J. Zakoian,et al.  GARCH Models: Structure, Statistical Inference and Financial Applications , 2010 .

[38]  Guglielmo Maria Caporale,et al.  Modelling Volatility of Cryptocurrencies Using Markov-Switching GARCH Models , 2018, Research in International Business and Finance.

[39]  E. Ruiz,et al.  Robust Bootstrap Densities for Dynamic Conditional Correlations: Implications for Portfolio Selection and Value-at-Risk , 2017 .

[40]  E. Ruiz,et al.  Robust bootstrap forecast densities for GARCH returns and volatilities , 2017 .

[41]  R. Engle,et al.  A Permanent and Transitory Component Model of Stock Return Volatility , 1993 .

[42]  Tim Bollerslev,et al.  Glossary to ARCH (GARCH) , 2008 .

[43]  Anil K. Bera,et al.  A Class of Nonlinear ARCH Models , 1992 .

[44]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[45]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[46]  Daniel Peña,et al.  Estimating GARCH volatility in the presence of outliers , 2012 .

[47]  Drew D. Creal,et al.  Generalized autoregressive score models with applications ∗ , 2010 .

[48]  Luiz Koodi Hotta,et al.  Bootstrap prediction in univariate volatility models with leverage effect , 2016, Math. Comput. Simul..

[49]  E. Ruiz,et al.  Revisiting Several Popular GARCH Models with Leverage Effect: Differences and Similarities , 2012 .

[50]  Stavros Stavroyiannis,et al.  Value-at-Risk and related measures for the Bitcoin , 2018 .

[51]  Timo Teräsvirta,et al.  An Introduction to Univariate GARCH Models , 2006 .

[52]  Ludger Hentschel.  All in the family Nesting symmetric and asymmetric GARCH models , 1995 .

[53]  P. Hansen,et al.  Realized GARCH: A Joint Model of Returns and Realized Measures of Volatility , 2010 .

[54]  Konstantinos Gkillas,et al.  An application of extreme value theory to cryptocurrencies , 2018 .

[55]  Christian Francq,et al.  Bartlett's formula for a general class of nonlinear processes , 2009 .

[56]  GARCH Model With Fat-Tailed Distributions and Bitcoin Exchange Rate Returns , 2017 .

[57]  S. Nadarajah,et al.  GARCH Modelling of Cryptocurrencies , 2017 .

[58]  Luc BAUWENS,et al.  Handbook of Volatility Models and Their Applications , 2012 .

[59]  Christophe Croux,et al.  Robust M-Estimation of Multivariate GARCH models , 2010, Comput. Stat. Data Anal..

[60]  Tae-Hwy Lee,et al.  Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood , 2004 .

[61]  Nora Muler,et al.  Robust estimates for GARCH models , 2008 .

[62]  C. Granger,et al.  A long memory property of stock market returns and a new model , 1993 .

[63]  Bruno Feunou,et al.  The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation , 2012, Journal of Financial and Quantitative Analysis.

[64]  Neil Shephard,et al.  Realising the future: forecasting with high frequency based volatility (HEAVY) models , 2010 .

[65]  Michael McAleer,et al.  Realized Volatility: A Review , 2008 .

[66]  David Ardia,et al.  Regime Changes in Bitcoin GARCH Volatility Dynamics , 2018, Finance Research Letters.

[67]  Márcio Poletti Laurini,et al.  Volatility and return jumps in bitcoin , 2018, Economics Letters.

[68]  Paul H. Kupiec,et al.  Techniques for Verifying the Accuracy of Risk Measurement Models , 1995 .

[69]  Angelika I. Kokkinaki,et al.  Bitcoin Is Volatile! Isn't that Right? , 2014, BIS.

[70]  Fulvio Corsi,et al.  A Simple Approximate Long-Memory Model of Realized Volatility , 2008 .

[71]  M. Bartlett.  On the Theoretical Specification and Sampling Properties of Autocorrelated Time‐Series , 1946 .

[72]  Kevin Sheppard,et al.  Optimal combinations of realised volatility estimators , 2009 .

[73]  Julian Lorenz,et al.  A Statistical Risk Assessment of Bitcoin and Its Extreme Tail Behaviour , 2016 .

[74]  M. Elbeck,et al.  Bitcoins as an investment or speculative vehicle? A first look , 2015 .

[75]  Xiaoping Zhou,et al.  Forecasting VaR and ES using dynamic conditional score models and skew Student distribution , 2016 .

[76]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[77]  E. Ghysels,et al.  Série Scientifique Scientific Series Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies , 2022 .

[78]  S. Nadarajah,et al.  A Statistical Analysis of Cryptocurrencies , 2017 .

[79]  Andrew J. Patton.  Volatility Forecast Comparison Using Imperfect Volatility Proxies , 2006 .

[80]  Peter Reinhard Hansen,et al.  The Model Confidence Set , 2010 .

[81]  Michael W. Brandt,et al.  Range-Based Estimation of Stochastic Volatility Models , 2001 .