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Gram-Charlier densities: a multivariate approach

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  • Esther B. Del Brio
  • Trino-Manuel Niguez
  • Javier Perote

Abstract

This paper introduces a new family of multivariate distributions based on Gram-Charlier and Edgeworth expansions. This family encompasses many of the univariate semi-non-parametric densities proposed in financial econometrics as marginal of its different formulations. Within this family, we focus on the analysis of the specifications that guarantee positivity to obtain well-defined multivariate semi-non-parametric densities. We compare two different multivariate distributions of the family with the multivariate Edgeworth-Sargan, Normal, Student's t and skewed Student's t in an in- and out-of-sample framework for financial returns data. Our results show that the proposed specifications provide a reasonably good performance, and would therefore be of interest for applications involving the modelling and forecasting of heavy-tailed distributions.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 9 (2009)
Issue (Month): 7 ()
Pages: 855-868

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Handle: RePEc:taf:quantf:v:9:y:2009:i:7:p:855-868

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Related research

Keywords: Empirical finance; Econometrics of financial markets; Financial assets; VaR;

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Cited by:
  1. Gabrielsen, A. & Zagaglia, Paolo & Kirchner, A. & Liu, Z., 2012. "Forecasting Value-at-Risk with time-varying variance, skewness and kurtosis in an exponential weighted moving average framework," MPRA Paper 39294, University Library of Munich, Germany.
  2. Withers, Christopher S. & Nadarajah, Saralees, 2014. "The dual multivariate Charlier and Edgeworth expansions," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 76-85.
  3. Del Brio, Esther B. & Perote, Javier, 2012. "Gram–Charlier densities: Maximum likelihood versus the method of moments," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 531-537.
  4. Del Brio, Esther B. & Ñíguez, Trino-Manuel & Perote, Javier, 2011. "Multivariate semi-nonparametric distributions with dynamic conditional correlations," International Journal of Forecasting, Elsevier, vol. 27(2), pages 347-364, April.

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