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Forecasting the density of asset returns

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  • Trino-Manuel Niguez
  • Javier Perote

Abstract

In this paper we introduce a transformation of the Edgeworth-Sargan series expansion of the Gaussian distribution, that we call Positive Edgeworth-Sargan (PES). The main advantage of this new density is that it is well defined for all values in the parameter space, as well as it integrates up to one. We include an illustrative empirical application to compare its performance with other distributions, including the Gaussian and the Student's t, to forecast the full density of daily exchange-rate returns by using graphical procedures. Our results show that the proposed function outperforms the other two models for density forecasting, then providing more reliable value-at-risk forecasts.

Suggested Citation

  • Trino-Manuel Niguez & Javier Perote, 2004. "Forecasting the density of asset returns," STICERD - Econometrics Paper Series 479, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:479
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    1. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
    2. 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.
    3. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
    4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    5. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    6. 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.
    7. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    8. Angel León & Juan Mora, 1999. "Modelling conditional heteroskedasticity: Application to the "IBEX-35" stock-return index," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(3), pages 215-238.
    9. 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.
    10. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    11. Clive W.J. Granger, 1999. "Outline of forecast theory using generalized cost functions," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 161-173.
    12. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-448, May.
    13. 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 863-883, November.
    14. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    15. Hamilton, James D, 1991. "A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 27-39, January.
    16. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 133-152.
    17. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    18. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    19. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    20. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    21. Ángel León & Gonzalo Rubio & Gregorio Serna, 2004. "Autoregressive Conditional Volatility, Skewness And Kurtosis," Working Papers. Serie AD 2004-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    22. Javier Perote, 2004. "The multivariate Edgeworth-Sargan density," Spanish Economic Review, Springer;Spanish Economic Association, vol. 6(1), pages 77-96, April.
    23. Granger,Clive W. J., 1999. "Empirical Modeling in Economics," Cambridge Books, Cambridge University Press, number 9780521778251.
    24. 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.
    25. Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
    26. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    1. 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.

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    More about this item

    Keywords

    Density forecasting; Edgeworth-Sargan distribution; probability integral transformations; P-value plots; VaR;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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