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

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Author Info
Enrique Sentana () (CEMFI, Centro de Estudios Monetarios y Financieros)
Javier Mencía () (Banco de España)

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Abstract

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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Publisher Info
Paper provided by CEMFI in its series Working Papers with number wp2008_0804.

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Date of creation: Apr 2008
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Handle: RePEc:cmf:wpaper:wp2008_0804

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Related research
Keywords: Bootstrap; inequality constraints; kurtosis; normality tests; skewness; supremum test; underidentified parameters.;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January. [Downloadable!] (restricted)
  2. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-33, July. [Downloadable!] (restricted)
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  3. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443. [Downloadable!] (restricted)
  4. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July. [Downloadable!] (restricted)
  5. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Blackwell Publishing, vol. 62(4), pages 639-61, October. [Downloadable!] (restricted)
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  6. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Blackwell Publishing, vol. 71(4), pages 945-973, October. [Downloadable!] (restricted)
  9. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April. [Downloadable!] (restricted)
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  10. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  11. 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.
  12. 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. [Downloadable!] (restricted)
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  13. 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. [Downloadable!] (restricted)
  14. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June. [Downloadable!] (restricted)
  15. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September. [Downloadable!] (restricted)
  16. Enrique Sentana & Gabriele Fiorentini, 2007. "On The Efficiency And Consistency Of Likelihood Estimation In Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Enrique Sentana & Javier Mencía, 2008. "Multivariate Location-Scale Mixtures Of Normals And Mean-Variance-Skwness Portfolio Allocation," Working Papers wp2008_0805, CEMFI. [Downloadable!]
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