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Convolution-t Distributions

Author

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  • Peter Reinhard Hansen
  • Chen Tong

Abstract

We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody cluster structures with flexible nonlinear dependencies and heterogeneous marginal distributions. Importantly, convolution-t distributions have simple density functions that facilitate estimation and likelihood-based inference. The characteristic features of convolution-t distributions are found to be important in an empirical analysis of realized volatility measures and help identify their underlying factor structure.

Suggested Citation

  • Peter Reinhard Hansen & Chen Tong, 2024. "Convolution-t Distributions," Papers 2404.00864, arXiv.org.
    • Handle: RePEc:arx:papers:2404.00864
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    References listed on IDEAS

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    2. Peter Reinhard Hansen & Chen Tong, 2026. "Exact Likelihood Inference and Robust Filtering for Gauss-Cauchy Convolution Models," Papers 2605.01665, arXiv.org, revised May 2026.

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    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • 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
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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