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Unfolded GARCH models

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  • Liu, Xiaochun
  • Luger, Richard

Abstract

A new GARCH-type model for autoregressive conditional volatility, skewness, and kurtosis is proposed. The approach decomposes returns into their signs and absolute values, and specifies the joint distribution by combining a multiplicative error model for the absolute values, a dynamic binary choice model for the signs, and a copula function for their interaction. The conditional volatility and kurtosis are determined by innovations following a folded (or absolute) Student-t distribution with time-varying degrees of freedom, and separate time variation in conditional return skewness is achieved by allowing the copula parameter to be dynamic. Model estimation is performed with Bayesian methods using an adaptive Markov chain Monte Carlo algorithm. An empirical application to the returns on four major international stock market indices illustrates the statistical and economic significance of the new model for conditional higher moments.

Suggested Citation

  • Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.
  • Handle: RePEc:eee:dyncon:v:58:y:2015:i:c:p:186-217
    DOI: 10.1016/j.jedc.2015.06.007
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    Cited by:

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    2. Liu, Xiaochun, 2017. "An integrated macro-financial risk-based approach to the stressed capital requirement," Review of Financial Economics, Elsevier, vol. 34(C), pages 86-98.
    3. Liu, Xiaochun, 2019. "On tail fatness of macroeconomic dynamics," Journal of Macroeconomics, Elsevier, vol. 62(C).
    4. Stanislav Anatolyev & Nikolay Gospodinov, 2019. "Multivariate Return Decomposition: Theory and Implications," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 487-508, May.
    5. Simon Lalancette & Jean†Guy Simonato, 2017. "The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation," European Financial Management, European Financial Management Association, vol. 23(2), pages 325-354, March.
    6. Liu, Xiaochun, 2017. "Unfolded risk-return trade-offs and links to Macroeconomic Dynamics," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 1-19.
    7. Xiaochun Liu, 2018. "Structural Volatility Impulse Response Function and Asymptotic Inference," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(2), pages 316-339.
    8. Liu, Xiaochun, 2017. "Can macroeconomic dynamics explain the time variation of risk–return trade-offs in the U.S. financial market?," The Quarterly Review of Economics and Finance, Elsevier, vol. 66(C), pages 275-293.
    9. León, Ángel & Ñíguez, Trino-Manuel, 2021. "The transformed Gram Charlier distribution: Parametric properties and financial risk applications," Journal of Empirical Finance, Elsevier, vol. 63(C), pages 323-349.
    10. You, Yu & Liu, Xiaochun, 2020. "Forecasting short-run exchange rate volatility with monetary fundamentals: A GARCH-MIDAS approach," Journal of Banking & Finance, Elsevier, vol. 116(C).

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    More about this item

    Keywords

    Conditional skewness and kurtosis; Direction-of-change model; Absolute returns; Folded distribution; Copula model; Adaptive MCMC;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • 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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