Entropy densities with an application to autoregressive conditional skewness and kurtosis

Journal of Econometrics

Volumn 106, Issue 1, 2002, Pages 119-142

  Rockinger, Michael ^a   Jondeau, Eric ^b  

^a HEC PARIS   (France)

^b BANQUE DE FRANCE   (France)

Author keywords

GARCH; Semi nonparametric estimation; Time varying skewness and kurtosis

Indexed keywords

ENTROPY; FINANCE; MATHEMATICAL MODELS; METHOD OF MOMENTS; NUMERICAL METHODS; STATISTICAL TESTS;

KURTOSIS; SKEWNESS;

ECONOMICS;

EID: 0344669945     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(01)00092-6     Document Type: Article

References (37)

1. Abramowitz M., Stegun I.A. Handbook of Mathematical Functions. 1970;Dover Publications, Inc. New York.
2. Alhassid Y., Agmon N., Levine R.D. An upper bound for the entropy and its applications to the maximal entropy problem. Chemical Physics Letters. 53(1):1978;22-26.
3. Agmon N., Alhassid Y., Levine R.D. An algorithm for finding the distribution of maximal entropy. Journal of Computational Physics. 30:1979;250-259.
4. Agmon N., Alhassid Y., Levine R.D. The maximum entropy formalism. Levine R.D., Tribus M. The Maximum Entropy Formalism. 1979;207-209 MIT Press, Cambridge, MA.
5. Barton D.E., Dennis K.E.R. The conditions under which Gram-Charlier and Edgeworth curves are positive definite and unimodal. Biometrika. 39:1952;425-427.
6. Bera A.K., Higgins M.L. A class of nonlinear ARCH models. International Economic Review. 33(1):1992;137-158.
7. Bollerslev T. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics. 31(3):1986;307-328.
8. Bollerslev T. A conditional heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics. 69:1987;542-547.
9. Bollerslev T., Engle R.F., Nelson D.B. ARCH models. Engle R.F., McFadden D.L. Handbook of Econometrics, Vol. 4. 1994;2959-3038 Elsevier Science, Amsterdam.
10. Buchen P., Kelly M. The maximum entropy distribution of an asset inferred from option prices. Journal of Financial and Quantitative Analysis. 31(1):1996;143-159.
11. Davis P., Polonsky I. Numerical interpolation, differentiation and integration. Abramowitz M., Stegun I.A. Handbook of Mathematical Functions. 1970;875-924 U.S. Govt. Printing Office, Washington.
12. Engle R.F. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica. 50(4):1982;987-1007.
13. Engle R.F., Gonzales-Rivera G. Semiparametric ARCH models. Journal of Business and Economic Statistics. 9(4):1991;345-359.
14. Fletcher R. An overview of unconstrained optimization. Spedicato E. Algorithms for Continuous Optimization, Vol. XX. 1994;109-143 Kluwer Academic, Dordrecht, Netherland.
15. Gallant A.R., Tauchen G. Semi non-parametric estimation of conditionally constrained heterogenous processes: asset pricing applications. Econometrica. 57(5):1989;1091-1120.
16. Golan A., Judge G., Miller D. Maximum Entropy Econometrics: Robust Estimation with Limited Data. 1996;Wiley, Chichester.
17. Hansen B.E. Autoregressive conditional density estimation. International Economic Review. 35(3):1994;705-730.
18. Harvey C.R., Siddique A. Autoregressive conditional skewness. Journal of Financial and Quantitative Analysis. 34(3):1999;465-487.
19. Hawkins R.J., Rubinstein M., Daniell G.J. Reconstruction of the probability density function implicit in option prices from incomplete and noisy data. Hanson K.M., Silver R.N. Maximum Entropy and Bayesian Methods. 1996;1-8 Kluwer Academic Publishers, Netherlands.
20. Jaynes E.T. Information theory and statistical mechanics. Physical Review. 106(4):1957;620-630.
21. Jaynes E.T. On the rationale of maximum-entropy methods. Proceedings of the IEEE. 70(9):1982;939-952.
22. Johnson N.L., Kotz S., Balakrishnan N. Continuous univariate distribution. Vol. 1. 2nd Edition. 1994;Wiley, New York.
23. Jondeau E., Rockinger M. Gram-Charlier densities. Journal of Economic Dynamics and Control. 25(10):2001;1457-1483.
24. Kraus A., Litzenberger R.H. Skewness preference and the valuation of risk assets. Journal of Finance. 31(4):1976;1085-1100.
25. Mead L.R., Papanicolaou N. Maximum entropy in the problem of moments. Journal of Mathematical Physics. 25(8):1984;2404-2417.
26. Mittelhammer R.C., Judge G.G., Miller D.J. Econometric Foundations. 2000;Cambridge University Press, Cambridge, UK.
27. Nelson D.B. Conditional heteroskedasticity in asset returns - a new approach. Econometrica. 59(2):1991;347-370.
28. Nocedal J., Wright S.J. Numerical Optimization. 1999;Springer, New York, USA.
29. Ormoneit D., White H. An efficient algorithm to compute maximum entropy densities. Econometric Reviews. 18(2):1999;127-140.
30. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical Recipes in C: The Art of Scientific Computing. 1999;Cambridge University Press, Cambridge, UK.
31. Richardson M., Smith T. A test for multivariate normality in stock returns. Journal of Business. 66(2):1993;295-321.
32. Shannon, C.E., 1948. The mathematical theory of communication. Bell Systems Technical Journal 27, 379-423; 623-656.
33. Stutzer M. A simple nonparametric approach to derivative security valuation. Journal of Finance. 51(5):1996;1633-1652.
34. Wheeler J.C., Gordon R.G. Rigorous bounds for thermodynamic properties of harmonic solids. The Journal of Chemical Physics. 51(12):1969;5566-5583.
35. White H. Estimation, Inference, and Specification Analysis. 1994;Cambridge University Press, Cambridge, UK.
36. Zellner A., Highfield R.A. Calculation of maximum entropy distributions and approximation of marginal posterior distributions. Journal of Econometrics. 37(2):1988;195-209.
37. Zellner, A., Tobias, J., Ryu, H., 1997. Bayesian method of moments analysis of time series models with an application to forecasting turning points in output growth rates. (Estadística, 49-51, 152-157), pp. 3-63.