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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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    3. Stanislav Anatolyev & Nikolay Gospodinov, 2019. "Multivariate Return Decomposition: Theory and Implications," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 487-508, May.
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    8. 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.
    9. Liu, Xiaochun, 2017. "Unfolded risk-return trade-offs and links to Macroeconomic Dynamics," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 1-19.
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    11. 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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