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Vector autoregression models with skewness and heavy tails

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  • Sune Karlsson
  • Stepan Mazur
  • Hoang Nguyen

Abstract

With uncertain changes of the economic environment, macroeconomic downturns during recessions and crises can hardly be explained by a Gaussian structural shock. There is evidence that the distribution of macroeconomic variables is skewed and heavy tailed. In this paper, we contribute to the literature by extending a vector autoregression (VAR) model to account for a more realistic assumption of the multivariate distribution of the macroeconomic variables. We propose a general class of generalized hyperbolic skew Student's t distribution with stochastic volatility for the error term in the VAR model that allows us to take into account skewness and heavy tails. Tools for Bayesian inference and model selection using a Gibbs sampler are provided. In an empirical study, we present evidence of skewness and heavy tails for monthly macroeconomic variables. The analysis also gives a clear message that skewness should be taken into account for better predictions during recessions and crises.

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  • Sune Karlsson & Stepan Mazur & Hoang Nguyen, 2021. "Vector autoregression models with skewness and heavy tails," Papers 2105.11182, arXiv.org.
  • Handle: RePEc:arx:papers:2105.11182
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    Cited by:

    1. Tamás Kiss & Stepan Mazur & Hoang Nguyen & Pär Österholm, 2023. "Modeling the relation between the US real economy and the corporate bond‐yield spread in Bayesian VARs with non‐Gaussian innovations," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 347-368, March.
    2. Loperfido, Nicola, 2024. "The skewness of mean–variance normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    3. Katarzyna Budnik & Gerhard Rünstler, 2023. "Identifying structural VARs from sparse narrative instruments: Dynamic effects of US macroprudential policies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(2), pages 186-201, March.
    4. Andrea Renzetti, 2023. "Modelling and Forecasting Macroeconomic Risk with Time Varying Skewness Stochastic Volatility Models," Papers 2306.09287, arXiv.org, revised Nov 2023.
    5. Guljanov, Gaygysyz & Mutschler, Willi & Trede, Mark, 2022. "Pruned Skewed Kalman Filter and Smoother: With Application to the Yield Curve," Dynare Working Papers 78, CEPREMAP.
    6. Kiss, Tamás & Nguyen, Hoang & Österholm, Pär, 2022. "The Relation between the High-Yield Bond Spread and the Unemployment Rate in the Euro Area," Finance Research Letters, Elsevier, vol. 46(PA).
    7. Florian Huber & Gary Koop, 2023. "Fast and Order-invariant Inference in Bayesian VARs with Non-Parametric Shocks," Working Papers 2309, University of Strathclyde Business School, Department of Economics.
    8. Florian Huber & Massimiliano Marcellino, 2023. "Coarsened Bayesian VARs -- Correcting BVARs for Incorrect Specification," Papers 2304.07856, arXiv.org, revised May 2023.
    9. Kiss, Tamás & Mazur, Stepan & Nguyen, Hoang, 2022. "Predicting returns and dividend growth — The role of non-Gaussian innovations," Finance Research Letters, Elsevier, vol. 46(PA).
    10. Tamás Kiss & Hoang Nguyen & Pär Österholm, 2023. "Modelling Okun’s law: Does non-Gaussianity matter?," Empirical Economics, Springer, vol. 64(5), pages 2183-2213, May.
    11. Jetro Anttonen & Markku Lanne & Jani Luoto, 2024. "Statistically identified structural VAR model with potentially skewed and fat‐tailed errors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(3), pages 422-437, April.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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