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Distributional tests in multivariate dynamic models with Normal and Student t innovations

Author

Listed:
  • Javier Mencía

    () (Banco de España)

  • Enrique Sentana

    () (CEMFI)

Abstract

We derive Lagrange Multiplier and Likelihood Ratio specifi cation tests for the null hypotheses of multivariate normal and Student t innovations using the Generalised Hyperbolic distribution as our alternative hypothesis. We decompose the corresponding Lagrange Multiplier-type tests into skewness and kurtosis components, from which we obtain more powerful one-sided Kuhn-Tucker versions that are equivalent to the Likelihood Ratio test, whose asymptotic distribution we provide. We conduct detailed Monte Carlo exercises to study our proposed tests in finite samples. Finally, we present an empirical application to ten US sectoral stock returns, which indicates that their conditional distribution is mildly asymmetric and strongly leptokurtic.

Suggested Citation

  • Javier Mencía & Enrique Sentana, 2009. "Distributional tests in multivariate dynamic models with Normal and Student t innovations," Working Papers 0929, Banco de España;Working Papers Homepage.
  • Handle: RePEc:bde:wpaper:0929
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    File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/09/Fic/dt0929e.pdf
    File Function: First version, December 2009
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    Cited by:

    1. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
    2. 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.
    3. Gabriele Fiorentini & Enrique Sentana, 2009. "Dynamic Specification Tests for Static Factor Models," Working Papers wp2009_0912, CEMFI.
    4. Yusuke Kamishiro & Roberto Serrano, 2011. "Equilibrium Blocking in Large Quasilinear Economies," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 552-567, August.
    5. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
    6. Roberto Serrano, 2009. "On Watson's Non-Forcing Contracts and Renegotiation," Economics Bulletin, AccessEcon, vol. 29(3), pages 2350-2360.
    7. 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.
    8. Bontemps, Christian, 2013. "Moment-Based Tests for Discrete Distributions," IDEI Working Papers 772, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2014.
    9. Gabriele Fiorentini & Enrique Sentana, 2018. "Consistent non-Gaussian pseudo maximum likelihood estimators," Working Paper series 18-06, Rimini Centre for Economic Analysis.
    10. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, and Debt Valuation," Working Papers wp2009_0902, CEMFI.
    11. 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.
    12. 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.
    13. Gabriele Fiorentini & Enrique Sentana, 2012. "Tests for Serial Dependence in Static, Non-Gaussian Factor Models," Working Papers wp2012_1211, CEMFI.
    14. Dante Amengual & Enrique Sentana, 2015. "Is a Normal Copula the Right Copula?," Working Papers wp2015_1504, CEMFI.
    15. 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.
    16. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification? (Resumen)," Working Papers wp2009_0905, CEMFI.
    17. 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).

    More about this item

    Keywords

    Bootstrap; Inequality Constraints; Kurtosis; Normality Tests; Skewness; Supremum Test; Underidentifed parameters;

    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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