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Estimation and testing of dynamic models with generalised hyperbolic innovations

By Javier F. Mencia and Enrique Sentana


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

Topics: HG Finance, HB Economic Theory
Publisher: Financial Markets Group, London School of Economics and Political Science
Year: 2004
OAI identifier:
Provided by: LSE Research Online

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  3. (2002). A new class of multivariate skew densities, with application to GARCH models. doi
  4. (1995). A score test against one-sided alternatives. doi
  5. (1989). An easily implemented, generalized inverse gaussian generator. doi
  6. (1994). An omnibus test for univariate and multivariate normality. Working Paper W4&91, Nuffield College,
  7. (2003). Approximating the probability distribution of functions of random variables: A new approach. mimeo
  8. (1997). Asymptotic bias for quasi-maximumlikelihood estimators in conditional heteroskedasticity models. doi
  9. (1994). Autoregressive conditional density estimation. doi
  10. Calzolari (2003a). Maximum likelihood estimation and inference in multivariate conditionally heteroskedastic dynamic regression models with Student t innovations. doi
  11. Calzolari (2003b). The relative efficiency of pseudomaximum likelihood estimation and inference in conditionally heteroskedastic dynamic regression models. mimeo CEMFI.
  12. (1994). Continuous univariate distributions, doi
  13. (1980). Efficient tests for normality, heteroskedasticity, and serial independence of regression residuals. doi
  14. (1994). Empirical process methods in Econometrics. In doi
  15. (1993). Estimation and inference in econometrics. doi
  16. (1965). Handbook of mathematical functions. doi
  17. (1998). Hypothesis testing for some nonregular cases in econometrics.
  18. (1983). IdentiÞcation and lack of identiÞcation.
  19. (1993). Introduction to multiple time series analysis (2nd ed.).
  20. (1988). Matrix differential calculus with applications in statistics and econometrics. doi
  21. (1976). Maximum likelihood estimation for dependent observations. doi
  22. (1970). Measures of multivariate skewness and kurtosis with applications. doi
  23. (2002). Modeling asymmetry and excess kurtosis in stock return data. Working Paper 00-0123, doi
  24. (2003). Modeling fat tails and skewness in multivariate regression models. Unpublished Master Thesis CEMFI.
  25. (1969). On the theory and application of the general linear model. doi
  26. (2004). On the validity of the Jarque-Bera normality test in conditionally heteroskedastic dynamic regression models. doi
  27. (1992). Quasi maximum likelihood estimation and inference in dynamic models with time-varying covariances. doi
  28. (2000). Residual-based test for normality in autoregressions: asymptotic theory and simulation evidence. doi
  29. (1983). Small sample properties of alternative forms of the Lagrange Multiplier test. doi
  30. (1986). SpeciÞcation testing when score test statistics are identically zero. doi
  31. (1982). Statistical properties of the generalized inverse Gaussian distribution. doi
  32. (1998). Testing for GARCH effects: a one-sided approach. doi
  33. (2004). Testing normality: a GMM approach. doi
  34. (2001). Testing when a parameter is on the boundary of the mantained hypothesis. doi
  35. (1983). Tests for multivariate normality with Pearson alternatives. doi
  36. (1990). The distribution of a quadratic form in normal variables (Algorithm AS 256.3). doi
  37. (1986). The exact moments of a ratio of quadratic forms in normal variables. doi
  38. (1998). The generalised hyperbolic models: estimation, Þnancial derivatives and risk measurement. Unpublished Ph.D.
  39. (1999). The numerical reliability of econometric software. doi
  40. (1996). Which moments to match? doi

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