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Estimation and Testing of Dynamic Models with Generalised Hyperbolic Innovations

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Author Info
Enrique Sentana ()

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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 Financial Markets Group in its series FMG Discussion Papers with number dp502.

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Date of creation: Jun 2004
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Handle: RePEc:fmg:fmgdps:dp502

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References listed on IDEAS
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  1. Jurgen A Doornik & Henrik Hansen, . "An omnibus test for univariate and multivariate normalit," Economics Papers W4&91., Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  2. 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.
  3. 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)
    Other versions:
  4. Luc Bauwens & Sébastien Laurent, 2002. "A New Class of Multivariate skew Densities, with Application to GARCH Models," Computing in Economics and Finance 2002 5, Society for Computational Economics.
    Other versions:
  5. 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.
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  7. 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)
  8. Eric Ghysels & Anders Eriksson Lars Forsberg, 2004. "Approximating the probability distribution of functions of random variables: A new approach," Econometric Society 2004 Far Eastern Meetings 503, Econometric Society. [Downloadable!]
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  9. 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.
  10. 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)
  11. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
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  13. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  14. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241. [Downloadable!] (restricted)
  15. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November. [Downloadable!] (restricted)
  16. Neil Shephard & Ole E. Barndorff-Nielsen, 2001. "Normal Modified Stable Processes," Economics Series Working Papers 072, University of Oxford, Department of Economics. [Downloadable!]
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  17. 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)
  18. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October. [Downloadable!]
  19. 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.
  20. 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)
  21. 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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  22. 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)
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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. Abel Elizalde & Rafael Repullo, 2004. "Economic And Regulatory Capital. What Is The Difference?," Working Papers wp2004_0422, CEMFI. [Downloadable!]
    Other versions:
  2. Enrique Sentana & Giorgio Calzolari & Gabriele Fiorentini, 2004. "Indirect Estimation Of Conditionally Heteroskedastic Factor Models," Working Papers wp2004_0409, CEMFI. [Downloadable!]
  3. Javier Díaz-Giménez & Josep Pijoan-Mas, 2006. "Flat Tax Reforms In The U.S.: A Boon For The Income Poor," Working Papers wp2006_0611, CEMFI. [Downloadable!]
    Other versions:
  4. Aleix Calveras & Juan-José Ganuza & Gerard Llobet, 2005. "Regulation And Opportunism: How Much Activism Do We Need?," Working Papers wp2005_0508, CEMFI. [Downloadable!]
    Other versions:
  5. 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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  6. Beatriz Dominguez & Juan-José Ganuza & Gerard Llobet, 2006. "R&D In The Pharmaceutical Industry: A World Of Small Innovation," Working Papers wp2006_0601, CEMFI. [Downloadable!]
    Other versions:
  7. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109. [Downloadable!]
    Other versions:
  8. Giorgio Canarella & Stephen M. Miller & Stephen K. Pollard, 2008. "Dynamic Stock Market Interactions between the Canadian, Mexican, and the United States Markets: The NAFTA Experience," Working papers 2008-49, University of Connecticut, Department of Economics. [Downloadable!]
    Other versions:
  9. Jose Ceron & Javier Suarez, 2006. "Hot And Cold Housing Markets: International Evidence," Working Papers wp2006_0603, CEMFI. [Downloadable!]
    Other versions:
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