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Identification of structural multivariate GARCH models

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  • Hafner, Christian M.
  • Herwartz, Helmut
  • Maxand, Simone

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 M. & Herwartz, Helmut & Maxand, Simone, 2022. "Identification of structural multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 227(1), pages 212-227.
    • Handle: RePEc:eee:econom:v:227:y:2022:i:1:p:212-227
    DOI: 10.1016/j.jeconom.2020.07.019
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    Cited by:

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    3. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    4. 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.
    5. Hafner, Christian M. & Herwartz, Helmut, 2023. "Correlation impulse response functions," Finance Research Letters, Elsevier, vol. 57(C).
    6. 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.
    7. 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.
    8. 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).
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    More about this item

    Keywords

    Structural innovations; Identifying assumptions; MGARCH; Portfolio risk; Volatility transmission;
    All these keywords.

    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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