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Identification of structural multivariate GARCH models

Author

Listed:
  • Hafner, Christian

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Herwartz, Helmut

    (University of Goettingen, Germany)

  • Maxand, Simone

    (University of Helsinki, Finland)

Abstract

The class of multivariate GARCH models is widely used to quantify and monitor volatility and correlation dynamics of financial time series. While many specifications have been proposed in the literature, these models are typically silent about the system inherent transmission of implied orthogonalized shocks to vector returns. In a framework of non- Gaussian independent structural shocks, this paper proposes a loss statistic, based on higher order co-moments, to discriminate in a data-driven way between alternative structural assumptions about the transmission scheme, and hence identify the structural model. Consistency of identification is shown theoretically and via a simulation study. In its structural form, a four dimensional system comprising US and Latin American stock market returns points to a substantial volatility transmission from the US to the Latin American markets. The identified structural model improves the estimation of classical measures of portfolio risk, as well as corresponding variations.

Suggested Citation

  • Hafner, Christian & Herwartz, Helmut & Maxand, Simone, 2020. "Identification of structural multivariate GARCH models," LIDAM Reprints ISBA 2020032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2020032
    DOI: https://doi.org/10.1016/j.jeconom.2020.07.019
    Note: In: Journal of Econometrics - to appear (2020)
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    Cited by:

    1. Simos Meintanis & Bojana Milošević & Marko Obradović & Mirjana Veljović, 2024. "Goodness‐of‐fit tests for the multivariate Student‐t distribution based on i.i.d. data, and for GARCH observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 298-319, March.
    2. Simos G. Meintanis & Joseph Ngatchou-Wandji & Šárka Hudecová, 2025. "Omnibus diagnostic procedures for vector multiplicative errors models," Statistical Papers, Springer, vol. 66(2), pages 1-44, February.
    3. Manuel Carlos Nogueira & Mara Madaleno, 2022. "Are Sustainability Indices Infected by the Volatility of Stock Indices? Analysis before and after the COVID-19 Pandemic," Sustainability, MDPI, vol. 14(22), pages 1-13, November.
    4. Matthias R Fengler & Jeannine Polivka, 2025. "Structural Volatility Impulse Response Analysis," Journal of Financial Econometrics, Oxford University Press, vol. 23(2), pages 951-971.
    5. Manabu Asai & Chia-Lin Chang & Michael McAleer & Laurent Pauwels, 2021. "Asymptotic and Finite Sample Properties for Multivariate Rotated GARCH Models," Econometrics, MDPI, vol. 9(2), pages 1-21, May.
    6. Zema, Sebastiano Michele, 2022. "Directed acyclic graph based information shares for price discovery," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    7. Herwartz, Helmut & Roestel, Jan, 2022. "Asset prices, financial amplification and monetary policy: Structural evidence from an identified multivariate GARCH model," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 78(C).
    8. Qingrui Wang & Zhao Yao, 2025. "Bayesian influence diagnostics for a multivariate GARCH model," Statistical Papers, Springer, vol. 66(2), pages 1-27, February.
    9. Fengler, Matthias & Polivka, Jeannine, 2021. "Proxy-identification of a structural MGARCH model for asset returns," Economics Working Paper Series 2103, University of St. Gallen, School of Economics and Political Science, revised Oct 2024.
    10. Sijie Yao & Hui Zou & Haipeng Xing, 2024. "L 1 Regularization for High-Dimensional Multivariate GARCH Models," Risks, MDPI, vol. 12(2), pages 1-28, February.
    11. Fengler, Matthias & Polivka, Jeanine, 2022. "Identifying Structural Shocks to Volatility through a Proxy-MGARCH Model," VfS Annual Conference 2022 (Basel): Big Data in Economics 264010, Verein für Socialpolitik / German Economic Association.
    12. Hafner, Christian M. & Herwartz, Helmut, 2023. "Correlation impulse response functions," Finance Research Letters, Elsevier, vol. 57(C).
    13. Christian M. Hafner & Sabrine Majeri, 2022. "Analysis of cryptocurrency connectedness based on network to transaction volume ratios," Digital Finance, Springer, vol. 4(2), pages 187-216, September.
    14. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    15. Hafner, Christian M. & Herwartz, Helmut, 2023. "Asymmetric volatility impulse response functions," Economics Letters, Elsevier, vol. 222(C).
    16. Herwartz, Helmut & Wang, Shu, 2023. "Point estimation in sign-restricted SVARs based on independence criteria with an application to rational bubbles," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).

    More about this item

    Keywords

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    JEL classification:

    • 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
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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