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On the Relationship of Cryptocurrency Price with US Stock and Gold Price Using Copula Models

Author

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  • Jong-Min Kim

    (Statistics Discipline, University of Minnesota at Morris, Morris, MN 56267, USA)

  • Seong-Tae Kim

    (Department of Mathematics, North Carolina A&T State University, Greensboro, NC 27411, USA)

  • Sangjin Kim

    (Department of Management and Information Systems, Dong-A University, Busan 49236, Korea)

Abstract

This paper examines the relationship of the leading financial assets, Bitcoin, Gold, and S&P 500 with GARCH-Dynamic Conditional Correlation (DCC), Nonlinear Asymmetric GARCH DCC (NA-DCC), Gaussian copula-based GARCH-DCC (GC-DCC), and Gaussian copula-based Nonlinear Asymmetric-DCC (GCNA-DCC). Under the high volatility financial situation such as the COVID-19 pandemic occurrence, there exist a computation difficulty to use the traditional DCC method to the selected cryptocurrencies. To solve this limitation, GC-DCC and GCNA-DCC are applied to investigate the time-varying relationship among Bitcoin, Gold, and S&P 500. In terms of log-likelihood, we show that GC-DCC and GCNA-DCC are better models than DCC and NA-DCC to show relationship of Bitcoin with Gold and S&P 500. We also consider the relationships among time-varying conditional correlation with Bitcoin volatility, and S&P 500 volatility by a Gaussian Copula Marginal Regression (GCMR) model. The empirical findings show that S&P 500 and Gold price are statistically significant to Bitcoin in terms of log-return and volatility.

Suggested Citation

  • Jong-Min Kim & Seong-Tae Kim & Sangjin Kim, 2020. "On the Relationship of Cryptocurrency Price with US Stock and Gold Price Using Copula Models," Mathematics, MDPI, vol. 8(11), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1859-:d:433665
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    References listed on IDEAS

    as
    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. Dumitrescu, Elena-Ivona & Hurlin, Christophe, 2012. "Testing for Granger non-causality in heterogeneous panels," Economic Modelling, Elsevier, vol. 29(4), pages 1450-1460.
    3. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
    4. El Mamoun Amrouk & Stephanie-Carolin Grosche & Thomas Heckelei, 2020. "Interdependence between cash crop and staple food international prices across periods of varying financial market stress," Applied Economics, Taylor & Francis Journals, vol. 52(4), pages 345-360, January.
    5. Katsiampa, Paraskevi, 2019. "An empirical investigation of volatility dynamics in the cryptocurrency market," Research in International Business and Finance, Elsevier, vol. 50(C), pages 322-335.
    6. 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.
    7. Klein, Tony & Pham Thu, Hien & Walther, Thomas, 2018. "Bitcoin is not the New Gold – A comparison of volatility, correlation, and portfolio performance," International Review of Financial Analysis, Elsevier, vol. 59(C), pages 105-116.
    8. Aslanidis, Nektarios & Bariviera, Aurelio F. & Martínez-Ibañez, Oscar, 2019. "An analysis of cryptocurrencies conditional cross correlations," Finance Research Letters, Elsevier, vol. 31(C), pages 130-137.
    9. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    10. Basel Maraqa & Murad Bein, 2020. "Dynamic Interrelationship and Volatility Spillover among Sustainability Stock Markets, Major European Conventional Indices, and International Crude Oil," Sustainability, MDPI, vol. 12(9), pages 1-14, May.
    11. Guesmi, Khaled & Saadi, Samir & Abid, Ilyes & Ftiti, Zied, 2019. "Portfolio diversification with virtual currency: Evidence from bitcoin," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 431-437.
    12. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
    13. Chen, Yufeng & Qu, Fang, 2019. "Leverage effect and dynamics correlation between international crude oil and China’s precious metals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    14. Anna Denkowska & Stanisław Wanat, 2020. "A Tail Dependence-Based MST and Their Topological Indicators in Modeling Systemic Risk in the European Insurance Sector," Risks, MDPI, vol. 8(2), pages 1-22, April.
    15. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    16. Steve Hyun & Jimin Lee & Jong-Min Kim & Chulhee Jun, 2019. "What Coins Lead in the Cryptocurrency Market: Using Copula and Neural Networks Models," JRFM, MDPI, vol. 12(3), pages 1-14, August.
    17. Hao Chen & Zhixin Liu & Yinpeng Zhang & You Wu, 2020. "The Linkages of Carbon Spot-Futures: Evidence from EU-ETS in the Third Phase," Sustainability, MDPI, vol. 12(6), pages 1-18, March.
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    Cited by:

    1. Haffar, Adlane & Le Fur, Éric, 2022. "Time-varying dependence of Bitcoin," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 211-220.
    2. Karimi, Parinaz & Mirzaee Ghazani, Majid & Ebrahimi, Seyed Babak, 2023. "Analyzing spillover effects of selected cryptocurrencies on gold and brent crude oil under COVID-19 pandemic: Evidence from GJR-GARCH and EVT copula methods," Resources Policy, Elsevier, vol. 85(PB).
    3. Nagula, Pavan Kumar & Alexakis, Christos, 2022. "A new hybrid machine learning model for predicting the bitcoin (BTC-USD) price," Journal of Behavioral and Experimental Finance, Elsevier, vol. 36(C).
    4. Na Fu & Liyan Geng & Junhai Ma & Xue Ding, 2023. "Price, Complexity, and Mathematical Model," Mathematics, MDPI, vol. 11(13), pages 1-30, June.
    5. Balcilar, Mehmet & Ozdemir, Huseyin & Agan, Busra, 2022. "Effects of COVID-19 on cryptocurrency and emerging market connectedness: Empirical evidence from quantile, frequency, and lasso networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    6. Paeng, Seongcheol & Senteney, Dave & Yang, Taewon, 2024. "Spillover effects, lead and lag relationships, and stable coins time series," The Quarterly Review of Economics and Finance, Elsevier, vol. 95(C), pages 45-60.

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