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Conditional heteroskedasticity in crypto-asset returns

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  • Shaw, Charles

Abstract

In a recent contribution to the financial econometrics literature, Chu et al. (2017) provide the first examination of the time-series price behaviour of the most popular cryptocurrencies. However, insufficient attention was paid to correctly diagnosing the distribution of GARCH innovations. When these data issues are controlled for, their results lack robustness and may lead to either underestimation or overestimation of future risks. The main aim of this paper therefore is to provide an improved econometric specification. Particular attention is paid to correctly diagnosing the distribution of GARCH innovations by means of Kolmogorov type non-parametric tests and Khmaladze's martingale transformation. Numerical computation is carried out by implementing a Gauss-Kronrod quadrature. Parameters of GARCH models are estimated using maximum likelihood. For calculating P-values, the parametric bootstrap method is used. Further reference is made to the merits and demerits of statistical techniques presented in the related and recently published literature.

Suggested Citation

  • Shaw, Charles, 2018. "Conditional heteroskedasticity in crypto-asset returns," MPRA Paper 90437, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:90437
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    File URL: https://mpra.ub.uni-muenchen.de/90437/1/MPRA_paper_90437.pdf
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    References listed on IDEAS

    as
    1. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
    2. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    3. Balcombe, Kelvin & Fraser, Iain, 2017. "Do bubbles have an explosive signature in markov switching models?," Economic Modelling, Elsevier, vol. 66(C), pages 81-100.
    4. Corradi, Valentina & Swanson, Norman R., 2006. "Bootstrap conditional distribution tests in the presence of dynamic misspecification," Journal of Econometrics, Elsevier, vol. 133(2), pages 779-806, August.
    5. Marc Gronwald, 2014. "The Economics of Bitcoins - Market Characteristics and Price Jumps," CESifo Working Paper Series 5121, CESifo.
    6. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    7. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    8. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Olivier Scaillet & Adrien Treccani & Christopher Trevisan, 2020. "High-Frequency Jump Analysis of the Bitcoin Market," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 209-232.
    11. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    12. Hall, Stephen G & Psaradakis, Zacharias & Sola, Martin, 1999. "Detecting Periodically Collapsing Bubbles: A Markov-Switching Unit Root Test," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 143-154, March-Apr.
    13. Chappell, Daniel, 2018. "Regime heteroskedasticity in Bitcoin: A comparison of Markov switching models," MPRA Paper 90682, University Library of Munich, Germany.
    14. Caporale, Guglielmo Maria & Zekokh, Timur, 2019. "Modelling volatility of cryptocurrencies using Markov-Switching GARCH models," Research in International Business and Finance, Elsevier, vol. 48(C), pages 143-155.
    15. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    16. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521405515, January.
    17. Shi, Shuping & Arora, Vipin, 2012. "An application of models of speculative behaviour to oil prices," Economics Letters, Elsevier, vol. 115(3), pages 469-472.
    18. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    19. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    20. Chris Brooks & Apostolos Katsaris, 2005. "A Three-Regime Model of Speculative Behaviour: Modelling the Evolution of the S&P 500 Composite Index," Economic Journal, Royal Economic Society, vol. 115(505), pages 767-797, July.
    21. Ghoudi, Kilani & Rémillard, Bruno, 2014. "Comparison of specification tests for GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 291-300.
    22. Katsiampa, Paraskevi, 2017. "Volatility estimation for Bitcoin: A comparison of GARCH models," Economics Letters, Elsevier, vol. 158(C), pages 3-6.
    23. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    24. Aït-Sahalia, Yacine & Xiu, Dacheng, 2016. "Increased correlation among asset classes: Are volatility or jumps to blame, or both?," Journal of Econometrics, Elsevier, vol. 194(2), pages 205-219.
    25. Adrian (Wai-Kong) Cheung & Eduardo Roca & Jen-Je Su, 2015. "Crypto-currency bubbles: an application of the Phillips-Shi-Yu (2013) methodology on Mt. Gox bitcoin prices," Applied Economics, Taylor & Francis Journals, vol. 47(23), pages 2348-2358, May.
    26. Jeffrey Chu & Stephen Chan & Saralees Nadarajah & Joerg Osterrieder, 2017. "GARCH Modelling of Cryptocurrencies," JRFM, MDPI, vol. 10(4), pages 1-15, October.
    27. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    28. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
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    Cited by:

    1. Chappell, Daniel, 2018. "Regime heteroskedasticity in Bitcoin: A comparison of Markov switching models," MPRA Paper 90682, University Library of Munich, Germany.
    2. Shazia Salamat & Niu Lixia & Sobia Naseem & Muhammad Mohsin & Muhammad Zia-ur-Rehman & Sajjad Ahmad Baig, 2020. "Modeling cryptocurrencies volatility using GARCH models: a comparison based on Normal and Student's T-Error distribution," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 7(3), pages 1580-1596, March.

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    More about this item

    Keywords

    Autoregressive conditional heteroskedasticity (ARCH); generalized autoregressive conditional heteroskedasticity (GARCH); market volatility; nonlinear time series; Khmaladze transform.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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