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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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    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. 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).
    5. Na Fu & Liyan Geng & Junhai Ma & Xue Ding, 2023. "Price, Complexity, and Mathematical Model," Mathematics, MDPI, vol. 11(13), pages 1-30, June.

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