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Estimation and testing of dynamic models with generalised hyperbolic innovations

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  • Mencia, Javier F.
  • Sentana, Enrique

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.

Suggested Citation

  • Mencia, Javier F. & Sentana, Enrique, 2004. "Estimation and testing of dynamic models with generalised hyperbolic innovations," LSE Research Online Documents on Economics 24742, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:24742
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    1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    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. 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.
    4. 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.
    5. 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 532-546, October.
    6. 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.
    7. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    8. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
    9. 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.
    10. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    11. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    12. Jan R. Magnus, 1986. "The Exact Moments of a Ratio of Quadratic Forms in Normal Variables," Annals of Economics and Statistics, GENES, issue 4, pages 95-109.
    13. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    14. BAUWENS, Luc & LAURENT, Sébastien, 2002. "A new class of multivariate skew densities, with application to GARCH models," LIDAM Discussion Papers CORE 2002020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    16. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    17. R. W. Farebrother, 1990. "The Distribution of a Quadratic Form in Normal Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(2), pages 294-309, June.
    18. 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.
    19. 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.
    20. repec:adr:anecst:y:1986:i:4:p:05 is not listed on IDEAS
    21. 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 705-730, August.
    22. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
    23. H. D. Vinod & B. D. McCullough, 1999. "The Numerical Reliability of Econometric Software," Journal of Economic Literature, American Economic Association, vol. 37(2), pages 633-665, June.
    24. H. D. Vinod & B. D. McCullough, 1999. "Corrigenda: The Numerical Reliability of Econometric Software," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1565-1565, December.
    25. 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.
    26. Bera, A. & John, S., 1983. "Tests for multivariate normality with Pearson alternatives," LIDAM Reprints CORE 534, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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    4. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 61-75, January.
    5. Catania, Leopoldo & Grassi, Stefano, 2022. "Forecasting cryptocurrency volatility," International Journal of Forecasting, Elsevier, vol. 38(3), pages 878-894.
    6. Zaichao Du & Pei Pei, 2020. "Backtesting portfolio value‐at‐risk with estimated portfolio weights," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 605-619, September.
    7. Gabriele Fiorentini & Enrique Sentana, 2007. "On the Efficiency and Consistency of Likelihood Estimation in Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI.
    8. Chen, Heng & Fan, Yanqin & Wu, Jisong, 2014. "A flexible parametric approach for estimating switching regime models and treatment effect parameters," Journal of Econometrics, Elsevier, vol. 181(2), pages 77-91.
    9. Xin Zhang & Drew Creal & Siem Jan Koopman & Andre Lucas, 2011. "Modeling Dynamic Volatilities and Correlations under Skewness and Fat Tails," Tinbergen Institute Discussion Papers 11-078/2/DSF22, Tinbergen Institute.
    10. José Cerón & Javier Suarez, 2006. "Hot and Cold Housing Markets: International Evidence," Working Papers wp2006_0603, CEMFI.
    11. André Lucas & Bernd Schwaab & Xin Zhang, 2017. "Modeling Financial Sector Joint Tail Risk in the Euro Area," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 171-191, January.
    12. Aleix Calveras & Juan-José Ganuza & Gerard Llobet, 2005. "Regulation and Opportunism: How Much Activism Do We Need?," Working Papers wp2005_0508, CEMFI.
    13. Ole E. Barndorff-Nielsen & Neil Shephard, 2012. "Basics of Levy processes," Economics Papers 2012-W06, Economics Group, Nuffield College, University of Oxford.
    14. 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.
    15. 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.
    16. Ole Eiler Barndorff‐Nielsen & Robert Stelzer, 2005. "Absolute Moments of Generalized Hyperbolic Distributions and Approximate Scaling of Normal Inverse Gaussian Lévy Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 617-637, December.
    17. David Scott & Diethelm Würtz & Christine Dong & Thanh Tran, 2011. "Moments of the generalized hyperbolic distribution," Computational Statistics, Springer, vol. 26(3), pages 459-476, September.
    18. Tzougas, George & Karlis, Dimitris, 2020. "An EM algorithm for fitting a new class of mixed exponential regression models with varying dispersion," LSE Research Online Documents on Economics 104027, London School of Economics and Political Science, LSE Library.
    19. 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.
    20. André Lucas & Bernd Schwaab & Xin Zhang, 2014. "Conditional Euro Area Sovereign Default Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 271-284, April.
    21. Gonzalo, J. & Olmo, J., 2007. "The impact of heavy tails and comovements in downside-risk diversification," Working Papers 07/02, Department of Economics, City University London.
    22. Enrique Sentana & Giorgio Calzolari & Gabriele Fiorentini, 2004. "Indirect Estimation of Conditionally Heteroskedastic Factor Models," Working Papers wp2004_0409, CEMFI.
    23. Pei Pei, 2010. "Backtesting Portfolio Value-at-Risk with Estimated Portfolio Weights," CAEPR Working Papers 2010-010, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    24. Andre Lucas & Bernd Schwaab & Xin Zhang, 2013. "Measuring Credit Risk in a Large Banking System: Econometric Modeling and Empirics," Tinbergen Institute Discussion Papers 13-063/IV/DSF56, Tinbergen Institute, revised 13 Oct 2014.
    25. Schwaab, Bernd & Lucas, André & Zhang, Xin, 2013. "Conditional and joint credit risk," Working Paper Series 1621, European Central Bank.

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    More about this item

    Keywords

    Inequality constraints; Kurtosis; Multivariate normality test; Skewness; Student t; Tail dependence;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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