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

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  • 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.

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File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/09/Fic/dt0929e.pdf
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Bibliographic Info

Paper provided by Banco de Espa�a in its series Banco de Espa�a Working Papers with number 0929.

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Length: 64 pages
Date of creation: Dec 2009
Date of revision:
Handle: RePEc:bde:wpaper:0929

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

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References

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  1. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, Econometric Society, vol. 53(5), pages 1047-70, September.
  2. Russell Davidson & James G. MacKinnon, 1981. "Small Sample Properties of Alternative Forms of the Lagrange Multiplier Test," Working Papers, Queen's University, Department of Economics 439, Queen's University, Department of Economics.
  3. Frank Milne & Dilip Madan, 1991. "Option Pricing With V. G. Martingale Components," Working Papers, Queen's University, Department of Economics 1159, Queen's University, Department of Economics.
  4. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, Econometric Society, vol. 65(3), pages 587-600, May.
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  6. Magnus, J.R., 1986. "The exact moments of a ratio of quadratic forms in normal variables," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153219, Tilburg University.
  7. Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
  8. Sentana,E., 1995. "Quadratic Arch Models," Papers, Centro de Estudios Monetarios Y Financieros- 9517, Centro de Estudios Monetarios Y Financieros-.
  9. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, Elsevier, vol. 86(1), pages 97-127, June.
  10. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 21(4), pages 532-46, October.
  11. Sentana, E., 2000. "Factor Representing Portfolios in Large Asset Markets," Papers, Centro de Estudios Monetarios Y Financieros- 0001, Centro de Estudios Monetarios Y Financieros-.
  12. BAUWENS, Luc & LAURENT, Sébastien, . "A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1793, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 945-973.
  14. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2004. "On the validity of the Jarque-Bera normality test in conditionally heteroskedastic dynamic regression models," Economics Letters, Elsevier, Elsevier, vol. 83(3), pages 307-312, June.
  15. Jurgen A Doornik & Henrik Hansen, . "An omnibus test for univariate and multivariate normalit," Economics Papers W4&91., Economics Group, Nuffield College, University of Oxford.
  16. Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper Series, The Rimini Centre for Economic Analysis 38-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
  17. Lee, Lung-Fei & Chesher, Andrew, 1986. "Specification testing when score test statistics are identically zero," Journal of Econometrics, Elsevier, Elsevier, vol. 31(2), pages 121-149, March.
  18. Kilian, Lutz & Demiroglu, Ufuk, 2000. "Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 18(1), pages 40-50, January.
  19. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, Econometric Society, vol. 51(6), pages 1605-33, November.
  20. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, Econometric Society, vol. 68(2), pages 399-406, March.
  21. Enrique Sentana & Javier Mencía, 2008. "Multivariate Location-Scale Mixtures Of Normals And Mean-Variance-Skwness Portfolio Allocation," Working Papers, CEMFI wp2008_0805, CEMFI.
  22. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, Elsevier, vol. 30(1-2), pages 415-443.
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