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Estimation And Testing Of Dynamic Models With Generalised Hyperbolic Innovations

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

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Abstract

We analyse the Generalised Hyperbolic distribution as a model for fat tails and asymmetries in multivariate conditionally heteroskedastic dynamic regression models. We provide a standardised version of this distribution, obtain analytical expressions for the log-likelihood score, and explain how to evaluate the information matrix. In addition, we derive tests for the null hypotheses of multivariate normal and Student t innovations, and decompose them into skewness and kurtosis components, from which we obtain more powerful one-sided versions. Finally, we present an empirical illustration with UK sectorial stock returns, which suggests that their conditional distribution is asymmetric and leptokurtic.

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Paper provided by CEMFI in its series Working Papers with number wp2004_0411.

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Date of creation: Jun 2004
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Handle: RePEc:cmf:wpaper:wp2004_0411

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Related research
Keywords: Inequality constraints kurtosis multivariate normality test skewness Student t tail dependence.

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Find related papers by JEL classification:
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models

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  6. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August. [Downloadable!] (restricted)
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  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)
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  9. 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.
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  12. B. D. McCullough & H. D. Vinod, 1999. "The Numerical Reliability of Econometric Software," Journal of Economic Literature, American Economic Association, vol. 37(2), pages 633-665, June. [Downloadable!] (restricted)
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  15. 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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  16. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  17. 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)
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  19. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
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  5. Aleix Calveras & Juan-José Ganuza & Gerard Llobet, 2005. "Regulation And Opportunism: How Much Activism Do We Need?," Working Papers wp2005_0508, CEMFI. [Downloadable!]
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