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Multivariate dynamic intensity peaks‐over‐threshold models

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  • Nikolaus Hautsch
  • Rodrigo Herrera

Abstract

We propose a multivariate dynamic intensity peaks‐over‐threshold model to capture extremes in multivariate return processes. The random occurrence of extremes is modeled by a multivariate dynamic intensity model, while temporal clustering of their size is captured by an autoregressive multiplicative error model. Applying the model to daily returns of three major stock indexes yields strong empirical support for a temporal clustering of both the occurrence and the size of extremes. Backtesting value‐at‐risk and expected shortfall forecasts shows that the consideration of clustering effects and of feedback between the magnitudes and the intensity of extremes results in better forecasts of risk.

Suggested Citation

  • Nikolaus Hautsch & Rodrigo Herrera, 2020. "Multivariate dynamic intensity peaks‐over‐threshold models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(2), pages 248-272, March.
    • Handle: RePEc:wly:japmet:v:35:y:2020:i:2:p:248-272
    DOI: 10.1002/jae.2741
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    Cited by:

    1. Pushpa Dissanayake & Teresa Flock & Johanna Meier & Philipp Sibbertsen, 2021. "Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights," Mathematics, MDPI, vol. 9(21), pages 1-33, November.
    2. Herrera, Rodrigo & González, Sergio & Clements, Adam, 2018. "Mutual excitation between OECD stock and oil markets: A conditional intensity extreme value approach," The North American Journal of Economics and Finance, Elsevier, vol. 46(C), pages 70-88.
    3. Lin Han & Ivor Cribben & Stefan Trueck, 2022. "Extremal Dependence in Australian Electricity Markets," Papers 2202.09970, arXiv.org.
    4. Candia, Claudio & Herrera, Rodrigo, 2024. "An empirical review of dynamic extreme value models for forecasting value at risk, expected shortfall and expectile," Journal of Empirical Finance, Elsevier, vol. 77(C).
    5. Fuentes, Fernanda & Herrera, Rodrigo & Clements, Adam, 2025. "Tail risk dynamics of banks with score-driven extreme value models," Journal of Empirical Finance, Elsevier, vol. 81(C).
    6. Fuentes, Fernanda & Herrera, Rodrigo & Clements, Adam, 2023. "Forecasting extreme financial risk: A score-driven approach," International Journal of Forecasting, Elsevier, vol. 39(2), pages 720-735.

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