Multivariate Gram-Charlier Densities
AbstractThis paper introduces a new family of multivariate distributions based on Gram-Charlier and Edgeworth expansions. This family encompasses many of the univariate seminonparametric densities proposed in the financial econometrics as marginal distributions of the different formulations. Within this family, we focus on the specifications that guarantee positivity so obtaining a well-defined multivariate density. We compare different "positive" multivariate distributions of the family with the multivariate Edgeworth-Sargan, Normal and Student’s t in an in- and out-sample framework for financial returns data. Our results show that the proposed specifications provide a quite reasonably good performance being so of interest for applications involving the modelling and forecasting of heavy-tailed distributions.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 29073.
Date of creation: 2008
Date of revision:
Multivariate distributions; Gram-Charlier and Edgeworth-Sargan densities; MGARCH models; financial data;
Find related papers by JEL classification:
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
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- Corrado, Charles J & Su, Tie, 1996. "Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices," Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol. 19(2), pages 175-92, Summer.
- Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
- 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.
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Nabeya, Seiji, 2001. "APPROXIMATION TO THE LIMITING DISTRIBUTION OF t- AND F-STATISTICS IN TESTING FOR SEASONAL UNIT ROOTS," Econometric Theory, Cambridge University Press, vol. 17(04), pages 711-737, August.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
- Ángel León & Javier Mencía & Enrique Sentana, 2007.
"Parametric properties of semi-nonparametric distributions, with applications to option valuation,"
Banco de Espaï¿½a Working Papers
0707, Banco de Espa�a.
- LeÃ³n, Ãngel & MencÃa, Javier & Sentana, Enrique, 2009. "Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 176-192.
- Ángel León & Javier Mencía & Enrique Sentana, 2005. "Parametric Properties Of Semi-Nonparametric Distributions, With Applications To Option Valuation," Working Papers wp2005_0509, CEMFI.
- León, Ángel & Mencía, Javier & Sentana, Enrique, 2005. "Parametric Properties of Semi-Nonparametric Distributions, With Applications to Option Valuation," CEPR Discussion Papers 5435, C.E.P.R. Discussion Papers.
- Gallant, A.R. & Tauchen, G., 1988.
"Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications,"
88-59, Chicago - Graduate School of Business.
- Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
- Russell Davidson & James G. MacKinnon, 1994.
"Graphical Methods for Investigating the Size and Power of Hypothesis Tests,"
903, Queen's University, Department of Economics.
- Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
- 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.
- Sargan, J D, 1975. "Gram-Charlier Approximations Applied to t Ratios of k-Class Estimators," Econometrica, Econometric Society, vol. 43(2), pages 327-46, March.
- Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
- Victor Fenton & Gallant, A. Ronald, 1996.
"Qualitative and Asymptotic Performance of SNP Density Estimators,"
96-17, Duke University, Department of Economics.
- Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, vol. 74(1), pages 77-118, September.
- Ignacio Mauleon & Javier Perote, 2000. "Testing densities with financial data: an empirical comparison of the Edgeworth-Sargan density to the Student's t," The European Journal of Finance, Taylor & Francis Journals, vol. 6(2), pages 225-239.
- Arslan, Olcay, 2005. "A new class of multivariate distributions: Scale mixture of Kotz-type distributions," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 18-28, November.
- Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
- Javier Perote, 2004. "The multivariate Edgeworth-Sargan density," Spanish Economic Review, Springer, vol. 6(1), pages 77-96, April.
- Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-48, May.
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