Méthodes d'estimation pour des lois stables avec des applications en finance
Journal de la Société française de statistique, Volume 146 (2005) no. 4, pp. 23-54.
@article{JSFS_2005__146_4_23_0,
     author = {Alvarez, Alexander and Olivares, Pablo},
     title = {M\'ethodes d'estimation pour des lois stables avec des applications en finance},
     journal = {Journal de la Soci\'et\'e fran\c{c}aise de statistique},
     pages = {23--54},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {146},
     number = {4},
     year = {2005},
     language = {fr},
     url = {http://www.numdam.org/item/JSFS_2005__146_4_23_0/}
}
TY  - JOUR
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
SP  - 23
EP  - 54
VL  - 146
IS  - 4
PB  - Société française de statistique
UR  - http://www.numdam.org/item/JSFS_2005__146_4_23_0/
LA  - fr
ID  - JSFS_2005__146_4_23_0
ER  - 
%0 Journal Article
%A Alvarez, Alexander
%A Olivares, Pablo
%T Méthodes d'estimation pour des lois stables avec des applications en finance
%J Journal de la Société française de statistique
%D 2005
%P 23-54
%V 146
%N 4
%I Société française de statistique
%U http://www.numdam.org/item/JSFS_2005__146_4_23_0/
%G fr
%F JSFS_2005__146_4_23_0
Alvarez, Alexander; Olivares, Pablo. Méthodes d'estimation pour des lois stables avec des applications en finance. Journal de la Société française de statistique, Volume 146 (2005) no. 4, pp. 23-54. http://www.numdam.org/item/JSFS_2005__146_4_23_0/

[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] 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. | MR | Zbl

[3] Dumouchel W.H. (1971). Stable Distributions in Statistical Inference. PhD. thesis, Dept. of Statistics, Yale University. | MR

[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. | MR | Zbl

[5] Fama E. (1965). The behavior of stock prices. J. of Business, 38, 34-105.

[6] Fama E. and Roll R. (1971). Parameters Estimates for Symmetric Stable Distributions. Journal of the American Statistical Association, 66, 331-339. | Zbl

[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. | MR | Zbl

[8] Feuerverger A. and Mcdonnough P. (1981). On the efficiency of empirical characteristic function procedures. J. Roy. Stat. Soc, Ser B, 43, 20-27. | MR | Zbl

[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. | MR | Zbl

[10] Garcia R., Renault E. and Veredas D. (2004). Estimation of Stable Distributions by Indirect Inference. CORE Mimeo.

[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. | MR | Zbl

[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] Hill B. (1975). A simple approach to inference about the tail of a distribution. Annals of Statistics, 3, 1163-1174. | MR | Zbl

[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. | MR | Zbl

[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] 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. | MR | Zbl

[17] Kanter M. (1975). Stable densities under change of scale and total variations inequalities. Annals of Probability 3, 697-707. | MR | Zbl

[18] Knight J.L., Yu J. (2002). Empirical Characteristic Function in Time Series Estimation. Econometric Theory, 18, 691-721. | MR | Zbl

[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. | Zbl

[20] Koutrouvelis L.A. (1980). Regression-type estimation of the parameters of stable laws. Journal of the American Statistical Association, 75, 918-928. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | JFM | Numdam | MR

[24] Lévy-Véhel J. et Walter C. (2002). Les marchés fractals, PUF, Paris.

[25] Mandelbrot B.B. (1963). The Variation of Certain Speculative Prices. Journal of Business, 26, 394-419.

[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. | MR | Zbl

[27] Mason D.M. (1982). Laws of large numbers for sums of extreme values. The Annals of Probability, 10, 754-764. | MR | Zbl

[28] Mcculloch J.H. (1986). Simple consistent estimators of stable distribution parameters. Communications in Statistics. Simulation and Computation, 15, 1109-1136. | MR | Zbl

[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. | MR

[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. | MR | Zbl

[31] Mittnik S., Rachev S. (2001). Stable non-Gaussian models in finance and econometrics, Math. Comp. Modelling 34 no. 9-11. | Zbl

[32] Nolan J. (1996). An algorithm for evaluating stable densities in Zolotarev's (M) parametrization. Preprint American University Washington.

[33] Nolan J. ( 1996.) Numerical approximation of stable densities and distribution functions. Preprint American University Washington.

[34] Panton D. (1992). Cumulative distribution function values for symmetric standardized stable distributions. Statist. Simula. 21, 458-492. | Zbl

[35] Paulson A. S. and Delehanty T. A. (1993). Tables of the fractiles of the stable law. Technical Report, Renesselaer Polytechnic Institute, Troy, NY.

[36] Paulson A.S., Holcomb E.W. and Ieitch R. (1975). The estimation of the parameters of the stable laws. Biometrika, 62, 163-170. | MR | Zbl

[37] Press S.J. (1972). Applied Multivariate Analysis. Holt, Rinehart and Winston, Inc., New York. | MR | Zbl

[38] Press S.J. (1972). Estimation in univariate and multivariate stable distributions. J. Amer. Stat. Assoc., 67, 842-846. | MR | Zbl

[39] Royston P. (1992). Which measures of skewness and kurtosis are best ? Statistics in Medicine, 11, 333-343.

[40] Samorodnitsky G., Taqqu M.S. (1994). Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance Chapman &Hall. | MR | Zbl

[41] Vogel R.M. and Fennessey N.M. (1993). L-moment diagrams should replace product-moment diagrams. Water Resources Research, 29, 1745-1752.

[42] Weron R. (1996). On the Chambers-Mallows-Stuck method for simulating skewed stable random variables. Statistics and Probability Letters, 28, 165-171. | MR | Zbl

[43] Weron R. (2001). Performance of the estimators of Stable Laws. Working Paper.

[44] Worsdale G. (1975). Tables of cumulative distribution function for symmetric stable distributions. Appl. Statistics, 24, 123-131. | MR

[45] Zolotarev V.M. (1966). On representation of stable laws by integrals. Selected Translation in Mathematical Statistics and Probability, 6, 84-88. | Zbl

[46] Zolotarev V.M. (1986). One-dimensional stable distributions, Trans. of Math. Monographs, AMS Vol. 65. | MR | Zbl