Méthodes d'estimation pour des lois stables avec des applications en finance

Alexander Alvarez; Pablo Olivares

Journal de la société française de statistique (2005)

  • Volume: 146, Issue: 4, page 23-54
  • ISSN: 1962-5197

How to cite


Alvarez, Alexander, and Olivares, Pablo. "Méthodes d'estimation pour des lois stables avec des applications en finance." Journal de la société française de statistique 146.4 (2005): 23-54. <http://eudml.org/doc/199033>.

author = {Alvarez, Alexander, Olivares, Pablo},
journal = {Journal de la société française de statistique},
language = {fre},
number = {4},
pages = {23-54},
publisher = {Société française de statistique},
title = {Méthodes d'estimation pour des lois stables avec des applications en finance},
url = {http://eudml.org/doc/199033},
volume = {146},
year = {2005},

AU - Alvarez, Alexander
AU - Olivares, Pablo
TI - Méthodes d'estimation pour des lois stables avec des applications en finance
JO - Journal de la société française de statistique
PY - 2005
PB - Société française de statistique
VL - 146
IS - 4
SP - 23
EP - 54
LA - fre
UR - http://eudml.org/doc/199033
ER -


  1. [1] BROTHERS K. M., DUMOUCHEL W. H. and PAULSON A. S. (1983). Fractiles of the stable laws. Technical report, Rensselaer Polytechnic Institute, Troy, NY. 
  2. [2] CHAMBERS J.M., MALLOWS C.L. and STUCK B.W. (1976). A Method for simulating stable random variables. Journal of the American Statistical Association, 71, 340-344. Zbl0341.65003MR415982
  3. [3] DUMOUCHEL W.H. (1971). Stable Distributions in Statistical Inference. PhD. thesis, Dept. of Statistics, Yale University. Zbl0321.62017MR2620950
  4. [4] DUMOUCHEL W.H. (1973). On the Asymptotic Normality of the Maximum Likelihood Estimate when Sampling from a Stable Distribution. Annals of Statistics, 1, 948-957. Zbl0287.62013MR339376
  5. [5] FAMA E. (1965). The behavior of stock prices. J. of Business, 38, 34-105. 
  6. [6] FAMA E. and ROLL R. (1971). Parameters Estimates for Symmetric Stable Distributions. Journal of the American Statistical Association, 66, 331-339. Zbl0217.51404
  7. [7] FEUERVERGER A. (1990). An efficient resuit for the empirical characteristic function in stationary time-series models. The Canadian Journal of Statistics, 18, 155-161. Zbl0703.62096MR1067167
  8. [8] FEUERVERGER A. and McDONNOUGH P. (1981). On the efficiency of empirical characteristic function procedures. J. Roy. Stat. Soc, Ser B, 43, 20-27. Zbl0454.62034MR610372
  9. [9] FEUERVERGER A. and McDONNOUGH P. (1981). On efficient inference in symmetric stable laws and processes. In M. Csorgo, Dawson, D.A., Rao, N.J.K. and Saleh, A..K. (Editors) Statistics and Related topics, 109-122. Zbl0482.62036MR665270
  10. [10] GARCIA R., RENAULT E. and VEREDAS D. (2004). Estimation of Stable Distributions by Indirect Inference. CORE Mimeo. 
  11. [11] GOLDIE C.M. and SMITH R.L. (1987). Slow variation with remainder : Theory and applications, Quarterly Journal of Mathematics, Oxford, Second Ser, 38, 45-71. Zbl0611.26001MR876263
  12. [12] GREENWOOD J.A., LANDWEHR J. M., MATALAS N.C. and WALLIS J.R. (1979). Probability weighted moments : definition and relation to parameters of several distributions expressable in inverse form. Water Resources Research, 15, 1049-1054. 
  13. [13] HILL B. (1975). A simple approach to inference about the tail of a distribution. Annals of Statistics, 3, 1163-1174. Zbl0323.62033MR378204
  14. [14] HOLT D. and CROW E. (1973). Tables and graphs of the stable probability fonctions, J. Res. Nat. Bureau Standars, B. Math. Sci., 77b, 143-198. Zbl0276.62098MR391468
  15. [15] HOSKING J.R.M. and WALLIS J.R. (1997). Regional Frequency Analysis : an approach based on L-moments, Cambridge University Press, Cambridge, U.K. 
  16. [16] HOSKING J.R.M. (1990). L-moments : analysis and estimation of distributions using linear combinations of order statistics. J.R. Statist. Soc. B, 52, 105-124. Zbl0703.62018MR1049304
  17. [17] KANTER M. (1975). Stable densities under change of scale and total variations inequalities. Annals of Probability 3, 697-707. Zbl0323.60013MR436265
  18. [18] KNIGHT J.L., Yu J. (2002). Empirical Characteristic Function in Time Series Estimation. Econometric Theory, 18, 691-721. Zbl1109.62337MR1906331
  19. [19] KOGON S.M. and WILLIAMS D.B. (1998). Characteristic function based estimation of stable parameters. In Adler, R., Feldman, R. and Taqqu, M. (eds.) A Practical Guide to Heavy Tailed Data, Birkhauser, Boston, MA, 311-335. Zbl0946.62019
  20. [20] KOUTROUVELIS L.A. (1980). Regression-type estimation of the parameters of stable laws. Journal of the American Statistical Association, 75, 918-928. Zbl0449.62026MR600977
  21. [21] KOUTROUVELIS I.A. (1981). An iterative procedure for the estimation of the parameters of stable laws, Communications in Statistics. Simulation and Computation, 10, 17-28. Zbl0474.62028MR608513
  22. [22] LEITCH R.A. and PAULSON A.S. (1975). Estimation of stable law parameters : stock price behavior application. J. Amer. Statist. Assoc, 70, 690-697. Zbl0307.62022MR423660
  23. [23] LÉVY P. (1924). Théorie des erreurs. La loi de Gauss et les lois exceptionnelles. Bulletin de la Société Mathématique de France, 52, 49-85. Zbl51.0386.02MR1504839JFM51.0386.02
  24. [24] LÉVY-VÉHEL J. et WALTER C. (2002). Les marchés fractals, PUF, Paris. 
  25. [25] MANDELBROT B.B. (1963). The Variation of Certain Speculative Prices. Journal of Business, 26, 394-419. 
  26. [26] MARINELLI C. , RACHEV S.T., ROLL R. (2001). Subordinated exchange rate models : evidence for heavy tailed distributions and long-range dependence. Stable non-Gaussian models in finance and econometrics. Math. Comp. Modelling, 34, no. 9-11, 955-1001. Zbl1006.60011MR1858833
  27. [27] MASON D.M. (1982). Laws of large numbers for sums of extreme values. The Annals of Probability, 10, 754-764. Zbl0493.60039MR659544
  28. [28] MCCULLOCH J.H. (1986). Simple consistent estimators of stable distribution parameters. Communications in Statistics. Simulation and Computation, 15, 1109-1136. Zbl0612.62028MR876783
  29. [29] MCCULLOCH J.H. (1997). Measuring tail thickness in order to estimate the stable index α : a critique. Bussiness and Economie Statistics, 15, 74-81. MR1435386
  30. [30] MCCULLOCH J. H. and PANTON D.(1998). Tables of the maximally-skewed stable distributions. In R. Adler, R. Feldman, and M. Taqqu (Eds.), A Practical Guide to Heavy Tails : Statistical Techniques for Analyzing Heavy Tailed Distributions, 501-508. Zbl0927.60020MR1652283
  31. [31] MITTNIK S., RACHEV S. (2001). Stable non-Gaussian models in finance and econometrics, Math. Comp. Modelling 34 no. 9-11. Zbl0991.00020
  32. [32] NOLAN J. (1996). An algorithm for evaluating stable densities in Zolotarev's (M) parametrization. Preprint American University Washington. 
  33. [33] NOLAN J. ( 1996.) Numerical approximation of stable densities and distribution functions. Preprint American University Washington. 
  34. [34] PANTON D. (1992). Cumulative distribution function values for symmetric standardized stable distributions. Statist. Simula. 21, 458-492. Zbl0850.62178
  35. [35] PAULSON A. S. and DELEHANTY T. A. (1993). Tables of the fractiles of the stable law. Technical Report, Renesselaer Polytechnic Institute, Troy, NY. Zbl0609.62038
  36. [36] PAULSON A.S., HOLCOMB E.W. and IEITCH R. (1975). The estimation of the parameters of the stable laws. Biometrika, 62, 163-170. Zbl0309.62017MR375588
  37. [37] PRESS S.J. (1972). Applied Multivariate Analysis. Holt, Rinehart and Winston, Inc., New York. Zbl0276.62051MR420970
  38. [38] PRESS S.J. (1972). Estimation in univariate and multivariate stable distributions. J. Amer. Stat. Assoc., 67, 842-846. Zbl0259.62031MR362666
  39. [39] ROYSTON P. (1992). Which measures of skewness and kurtosis are best ? Statistics in Medicine, 11, 333-343. 
  40. [40] SAMORODNITSKY G., TAQQU M.S. (1994). Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance Chapman &Hall. Zbl0925.60027MR1280932
  41. [41] VOGEL R.M. and FENNESSEY N.M. (1993). L-moment diagrams should replace product-moment diagrams. Water Resources Research, 29, 1745-1752. 
  42. [42] WERON R. (1996). On the Chambers-Mallows-Stuck method for simulating skewed stable random variables. Statistics and Probability Letters, 28, 165-171. Zbl0856.60022MR1394670
  43. [43] WERON R. (2001). Performance of the estimators of Stable Laws. Working Paper. 
  44. [44] WORSDALE G. (1975). Tables of cumulative distribution function for symmetric stable distributions. Appl. Statistics, 24, 123-131. MR388715
  45. [45] ZOLOTAREV V.M. (1966). On representation of stable laws by integrals. Selected Translation in Mathematical Statistics and Probability, 6, 84-88. Zbl0202.48901
  46. [46] ZOLOTAREV V.M. (1986). One-dimensional stable distributions, Trans. of Math. Monographs, AMS Vol. 65. Zbl0589.60015MR854867

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.