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What They Did Not Tell You About Algebraic (Non-)Existence, Mathematical (IR-)Regularity and (Non-)Asymptotic Properties of the Dynamic Conditional Correlation (DCC) Model

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  • Michael McAleer

    ( Department of Quantitative Finance National Tsing Hua University, Taiwan and Econometric Institute Erasmus School of Economics Erasmus University Rotterdam, The Netherlands and Department of Quantitative Economics Complutense University of Madrid, Spain And Institute of Advanced Sciences Yokohama National University, Japan.)

Abstract

In order to hedge efficiently, persistently high negative covariances or, equivalently, correlations, between risky assets and the hedging instruments are intended to mitigate against financial risk and subsequent losses. If there is more than one hedging instrument, multivariate covariances and correlations will have to be calculated. As optimal hedge ratios are unlikely to remain constant using high frequency data, it is essential to specify dynamic time-varying models of covariances and correlations. These values can either be determined analytically or numerically on the basis of highly advanced computer simulations. Analytical developments are occasionally promulgated for multivariate conditional volatility models. The primary purpose of the paper is to analyse purported analytical developments for the only multivariate dynamic conditional correlation model to have been developed to date, namely Engle’s (2002) widely-used Dynamic Conditional Correlation (DCC) model. Dynamic models are not straightforward (or even possible) to translate in terms of the algebraic existence, underlying stochastic processes, specification, mathematical regularity conditions, and asymptotic properties of consistency and asymptotic normality, or the lack thereof. The paper presents a critical analysis, discussion, evaluation and presentation of caveats relating to the DCC model, and an emphasis on the numerous dos and don’ts in implementing the DCC and related model in practice.

Suggested Citation

  • Michael McAleer, 2019. "What They Did Not Tell You About Algebraic (Non-)Existence, Mathematical (IR-)Regularity and (Non-)Asymptotic Properties of the Dynamic Conditional Correlation (DCC) Model," Documentos de Trabajo del ICAE 2019-17, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:1917
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    1. Michael McAleer, 2019. "What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity and (Non-) Asymptotic Properties of the Full BEKK Dynamic Conditional Covariance Model," JRFM, MDPI, vol. 12(2), pages 1-7, April.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    3. Michael McAleer, 2014. "Asymmetry and Leverage in Conditional Volatility Models," Econometrics, MDPI, vol. 2(3), pages 1-6, September.
    4. Massimiliano Caporin & Michael McAleer, 2012. "Do We Really Need Both Bekk And Dcc? A Tale Of Two Multivariate Garch Models," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 736-751, September.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Michael McAleer, 2019. "What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity, and (Non-) Asymptotic Properties of the Dynamic Conditional Correlation (DCC) Model," JRFM, MDPI, vol. 12(2), pages 1-9, April.
    7. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things you should know about DCC," Tinbergen Institute Discussion Papers 13-048/III, Tinbergen Institute.
    8. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things You Should Know about the Dynamic Conditional Correlation Representation," Econometrics, MDPI, vol. 1(1), pages 1-12, June.
    9. Oecd, 2002. "Access for Business," OECD Digital Economy Papers 67, OECD Publishing.
    10. McAleer, Michael & Chan, Felix & Hoti, Suhejla & Lieberman, Offer, 2008. "Generalized Autoregressive Conditional Correlation," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1554-1583, December.
    11. 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.
    12. 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.
    13. Gian Piero Aielli, 2011. "Dynamic Conditional Correlation: On properties and estimation," "Marco Fanno" Working Papers 0142, Dipartimento di Scienze Economiche "Marco Fanno".
    14. 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.
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    Cited by:

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    2. Michael McAleer, 2019. "What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity, and (Non-) Asymptotic Properties of the Dynamic Conditional Correlation (DCC) Model," JRFM, MDPI, vol. 12(2), pages 1-9, April.
    3. Hafner, Christian M. & Herwartz, Helmut & Maxand, Simone, 2022. "Identification of structural multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 227(1), pages 212-227.
    4. Asai, Manabu & Gupta, Rangan & McAleer, Michael, 2020. "Forecasting volatility and co-volatility of crude oil and gold futures: Effects of leverage, jumps, spillovers, and geopolitical risks," International Journal of Forecasting, Elsevier, vol. 36(3), pages 933-948.
    5. Yu-Ann Wang & Chia-Lin Chang, 2024. "Portfolio selection from risk transfer mechanisms in a time of crisis for renewable energy markets," KIER Working Papers 1108, Kyoto University, Institute of Economic Research.
    6. Zolfaghari, Mehdi & Ghoddusi, Hamed & Faghihian, Fatemeh, 2020. "Volatility spillovers for energy prices: A diagonal BEKK approach," Energy Economics, Elsevier, vol. 92(C).
    7. Michael McAleer, 2019. "What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity and (Non-) Asymptotic Properties of the Full BEKK Dynamic Conditional Covariance Model," JRFM, MDPI, vol. 12(2), pages 1-7, April.
    8. Aloui, Chaker & Hamida, Hela ben & Yarovaya, Larisa, 2021. "Are Islamic gold-backed cryptocurrencies different?," Finance Research Letters, Elsevier, vol. 39(C).
    9. Chia-Lin Chang & Michael McAleer & Jiarong Tian, 2019. "Modeling and Testing Volatility Spillovers in Oil and Financial Markets for the USA, the UK, and China," Energies, MDPI, vol. 12(8), pages 1-24, April.
    10. Das, Sonali & Demirer, Riza & Gupta, Rangan & Mangisa, Siphumlile, 2019. "The effect of global crises on stock market correlations: Evidence from scalar regressions via functional data analysis," Structural Change and Economic Dynamics, Elsevier, vol. 50(C), pages 132-147.
    11. Semei Coronado & Rangan Gupta & Besma Hkiri & Omar Rojas, 2020. "Time-Varying Spillovers between Currency and Stock Markets in the USA: Historical Evidence From More than Two Centuries," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(4), pages 44-76, December.
    12. Konstantinos Gkillas & Christoforos Konstantatos & Costas Siriopoulos, 2021. "Uncertainty Due to Infectious Diseases and Stock–Bond Correlation," Econometrics, MDPI, vol. 9(2), pages 1-18, April.
    13. Hou, Yang (Greg) & Li, Steven, 2020. "Volatility and skewness spillover between stock index and stock index futures markets during a crash period: New evidence from China," International Review of Economics & Finance, Elsevier, vol. 66(C), pages 166-188.
    14. Katsiampa, Paraskevi & Yarovaya, Larisa & Zięba, Damian, 2022. "High-frequency connectedness between Bitcoin and other top-traded crypto assets during the COVID-19 crisis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 79(C).
    15. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2022. "Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers," Journal of Econometrics, Elsevier, vol. 227(1), pages 285-304.
    16. Mai, Te-Ke & Foley, Aoife M. & McAleer, Michael & Chang, Chia-Lin, 2022. "Impact of COVID-19 on returns-volatility spillovers in national and regional carbon markets in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 169(C).
    17. Hsu, Shu-Han & Sheu, Chwen & Yoon, Jiho, 2021. "Risk spillovers between cryptocurrencies and traditional currencies and gold under different global economic conditions," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).

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    More about this item

    Keywords

    Hedging; Covariances; Correlations; Existence; Mathematical regularity; Invertibility; Likelihood function; Statistical asymptotic properties; Caveats; Practical implementation.;
    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
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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