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Distributional Tests in Multivariate Dynamic Models with Normal and Student-t Innovations

Author

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  • Javier Mencía

    (Bank of Spain)

  • Enrique Sentana

    (CEMFI)

Abstract

We derive Lagrange multiplier and likelihood ratio specification tests for the null hypotheses of multivariate normal and Student-t innovations using the generalized hyperbolic distribution as our alternative hypothesis. We decompose the corresponding Lagrange multiplier-type tests into skewness and kurtosis components. We also obtain more powerful one-sided Kuhn-Tucker versions that are equivalent to the likelihood ratio test, whose asymptotic distribution we provide. Finally, we conduct detailed Monte Carlo exercises to study the size and power properties of our proposed tests in finite samples. © 2011 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Suggested Citation

  • Javier Mencía & Enrique Sentana, 2012. "Distributional Tests in Multivariate Dynamic Models with Normal and Student-t Innovations," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 133-152, February.
  • Handle: RePEc:tpr:restat:v:94:y:2012:i:1:p:133-152
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    Cited by:

    1. Yusuke Kamishiro & Roberto Serrano, 2011. "Equilibrium Blocking in Large Quasilinear Economies," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 552-567, August.
    2. Roberto Serrano, 2009. "On Watson's Non-Forcing Contracts and Renegotiation," Economics Bulletin, AccessEcon, vol. 29(3), pages 2350-2360.
    3. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification? (Resumen)," Working Papers wp2009_0905, CEMFI.
    4. Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, vol. 153(2), pages 105-121, December.
    5. Chen, Heng & Fan, Yanqin & Wu, Jisong, 2014. "A flexible parametric approach for estimating switching regime models and treatment effect parameters," Journal of Econometrics, Elsevier, vol. 181(2), pages 77-91.
    6. Prosper Dovonon, 2013. "Conditionally Heteroskedastic Factor Models With Skewness And Leverage Effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1110-1137, November.
    7. Dante Amengual & Enrique Sentana, 2015. "Is a Normal Copula the Right Copula?," Working Papers wp2015_1504, CEMFI.
    8. Roland Pongou & Roberto Serrano, 2009. "A dynamic theory of fidelity networks with an application to the spread of HIV/AIDS," Working Papers 2009-03, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    9. Bontemps, Christian, 2013. "Moment-Based Tests for Discrete Distributions," IDEI Working Papers 772, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2014.
    10. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.
    11. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, pages 367-391.
    12. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
    13. Alexios Ghalanos & Eduardo Rossi & Giovanni Urga, 2015. "Independent Factor Autoregressive Conditional Density Model," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 594-616, May.
    14. Gabriele Fiorentini & Enrique Sentana, 2009. "Dynamic Specification Tests for Static Factor Models," Working Papers wp2009_0912, CEMFI.
    15. Rafael Repullo & Jesús Saurina & Carlos Trucharte, 2010. "Mitigating the pro-cyclicality of Basel II," Economic Policy, CEPR;CES;MSH, pages 659-702.
    16. Bontemps, Christian, 2014. "Simple moment-based tests for value-at-risk models and discrete distribution," TSE Working Papers 14-535, Toulouse School of Economics (TSE).
    17. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
    18. Josep Pijoan-Mas & José-Víctor Ríos-Rull, 2014. "Heterogeneity in Expected Longevities," Demography, Springer;Population Association of America (PAA), pages 2075-2102.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • 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

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