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Distributional Tests In Multivariate Dynamic Models With Normal And Student T Innovations

We derive specification tests for the null hypotheses of multivariate normal and Student t innovations using the Generalised Hyperbolic distribution as our alternative hypothesis. In both cases, 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 asymptotically equivalent to the Likelihood Ratio test. We conduct detailed Monte Carlo exercises that compare our proposed tests with their competitors 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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Paper provided by CEMFI in its series Working Papers with number wp2008_0804.

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Date of creation: Apr 2008
Date of revision:
Handle: RePEc:cmf:wpaper:wp2008_0804
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  1. Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
  2. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
  3. BONTEMPS, Christian & MEDDAHI, Nour, 2002. "Testing Normality : A GMM Approach," Cahiers de recherche 2002-14, Universite de Montreal, Departement de sciences economiques.
  4. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55.
  5. Enrique Sentana & Javier Mencía, 2008. "Multivariate Location-Scale Mixtures Of Normals And Mean-Variance-Skwness Portfolio Allocation," Working Papers wp2008_0805, CEMFI.
  6. 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, vol. 21(4), pages 532-46, October.
  7. Jurgen A Doornik & Henrik Hansen, . "An omnibus test for univariate and multivariate normalit," Economics Papers W4&91., Economics Group, Nuffield College, University of Oxford.
  8. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April.
  9. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
  10. 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, vol. 18(1), pages 40-50, January.
  11. Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper Series 38-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
  12. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 62(4), pages 639-61, October.
  13. BAUWENS, Luc & LAURENT, Sébastien, . "A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models," CORE Discussion Papers RP 1793, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  15. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 945-973.
  16. Davidson, Russel & MacKinnon, James G., 1983. "Small sample properties of alternative forms of the Lagrange Multiplier test," Economics Letters, Elsevier, vol. 12(3-4), pages 269-275.
  17. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
  18. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  19. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
  20. 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, vol. 83(3), pages 307-312, June.
  21. Lee, Lung-Fei & Chesher, Andrew, 1986. "Specification testing when score test statistics are identically zero," Journal of Econometrics, Elsevier, vol. 31(2), pages 121-149, March.
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