Advanced Search
MyIDEAS: Login

Gram–Charlier densities: Maximum likelihood versus the method of moments

Contents:

Author Info

  • Del Brio, Esther B.
  • Perote, Javier

Abstract

This paper compares two alternative estimation methods for estimating the density underlying financial returns specified in terms of a finite Gram–Charlier (GC) expansion. Maximum likelihood (ML) is the most widely employed method despite the fact that it is only consistent under the Gaussian or the true density, and usually involves convergence problems. Alternatively, the method of moments (MM) is a natural and straightforward procedure, although positivity is only guaranteed in the asymptotic expansion. We show an example for estimating daily returns of the Dow Jones Index with a very long data set, illustrating that both ML and MM yield similar outcomes. Therefore the MM applied to GC densities should be considered as an accurate tool for risk management and forecasting.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.sciencedirect.com/science/article/pii/S0167668712000844
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 51 (2012)
Issue (Month): 3 ()
Pages: 531-537

as in new window
Handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:531-537

Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/505554

Related research

Keywords: Semi-nonparametric method; Maximum likelihood; Method of moments; Financial returns density; Value at risk;

Find related papers by JEL classification:

References

References listed on IDEAS
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.:
as in new window
  1. 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.
  2. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  3. Leon, Angel & Rubio, Gonzalo & Serna, Gregorio, 2005. "Autoregresive conditional volatility, skewness and kurtosis," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 599-618, September.
  4. 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.
  5. Esther B. Del Brio & Trino-Manuel Niguez & Javier Perote, 2009. "Gram-Charlier densities: a multivariate approach," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 855-868.
  6. 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.
  7. T M Niguez & I Paya & D Peel & J Perote, 2011. "On the stability of the CRRA utility under high degrees of uncertainty," Working Papers 615773, Lancaster University Management School, Economics Department.
  8. Arnold Polanski & Evarist Stoja, 2010. "Incorporating higher moments into value-at-risk forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(6), pages 523-535.
  9. Carlos Velasco & Peter M. Robinson, 2001. "Edgeworth expansions for spectral density estimates and studentized sample mean," LSE Research Online Documents on Economics 315, London School of Economics and Political Science, LSE Library.
  10. Trino-Manuel Ñíguez & Javier Perote, 2012. "Forecasting Heavy-Tailed Densities with Positive Edgeworth and Gram-Charlier Expansions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(4), pages 600-627, 08.
  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  12. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
  13. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  14. Javier Perote, 2004. "The multivariate Edgeworth-Sargan density," Spanish Economic Review, Springer, vol. 6(1), pages 77-96, April.
  15. Phillips, Peter C B, 1977. "A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators," Econometrica, Econometric Society, vol. 45(6), pages 1517-34, September.
  16. 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.
  17. 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.
  18. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
  19. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  20. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
  21. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-48, May.
  22. E.K. Berndt & B.H. Hall & R.E. Hall, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 103-116 National Bureau of Economic Research, Inc.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2014. "Semi-nonparametric VaR forecasts for hedge funds during the recent crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 330-343.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:531-537. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.