Data analysis for heavy tailed multivariate samples

Communications in Statistics. Part C: Stochastic Models

Volumn 13, Issue 4, 1997, Pages 687-702

  Nolan, John P ^a   Panorska, Anna K ^a  

^a AMERICAN UNIVERSITY   (United States)

Author keywords

Estimation; Heavy tail modeling; Multivariate stable distributions; Spectral measure

Indexed keywords

EID: 0003286308     PISSN: 08820287     EISSN: None     Source Type: Journal    
DOI: 10.1080/15326349708807447     Document Type: Article

References (38)

1. Byczkowski, T., Nolan, J. P., and Rajput, B. (1993), "Approximation of Multidimensional Stable Densities," Journal of Multivariate Analysis, 46:13-31.
2. Cheng, B.N., and Rachev, S.T., (1995), "Multivariate stable securities in financial markets", Mathematical Finance (to appear).
3. Fama, E., (1965), "The behavior of Stock Market Prices" Journal Business, 38:34-105.
4. DuMouchel, W. (1975), "Stable Distributions in Statistical Inference 2: Information from Stably Distributed Samples", JASA 70:386-393.
5. Easton, G. S., and McCulloch, R. E. (1990), "A multivariate generalization of quantile-quantile plots" JASA 85: 376-386.
6. Embrechts, P., Klüppelberg, C., and Mikosch, T., (1996), Modelling Extremal Events with Emphasis on Insurance and Finance, book manuscript, (to appear in Springer-Verlag, Berlin).
7. Hill, B. (1975), "A Simple Approach to Inference about the Tail of a Distribution", Ann. Stat., 3, 1163-1174.
8. Janicki, A., and Weron, A., (1994), Simulation and Chaotic Behavior of α-stable Stochastic Processes, Marcel Dekker, N.Y.
9. Jurlewicz, A., Weron, A., Weron, K. (1996), "Asymptotic Behaviour of Stochastic Systems with Conditionally Exponential Decay Property", Appl. Math, 23:379-394.
10. Kim, J. R., Mittnik, S., and Rachev, S. T. (1996), "Econometrics with α- stable Innovation Processes", (preprint).
11. Kozubowski, T. J., and Rachev, S. T. (1994), "The Theory of Geometric Stable Distributions and its Use in Modeling Financial Data," European Journal of Operational Research, 74:310-324.
12. Kratz, M. F. , and Resnick, S.I. (1996), "The QQ- Estimator and Heavy Tails", Stoch. Models, (to appear).
13. Mandelbrot, B. (1963), "The Variation of Certain Speculative Prices", Journal of Business, 26:394-419.
14. McCulloch, J. H. (1986), "Simple Consistent Estimators of Stable Distribution Parameters," Commun. in Stat. Simula., 15:1109-1136.
15. McCulloch, J. H. (1994a), "Estimation of bivariate stable spectral densities," Technical Report, Department of Economics, Ohio State Univertsity.
16. McCulloch, J. H. (1994b), "Numerical Approximation of the Symmetric Stable Distribution and Density", Technical Report, Department of Economics, Ohio State University.
17. McCulloch, J. H. (1996), "Financial Applications of Stable Distributions," Statistical Methods in Finance, Handbook of Statistics, Volume 14, Edited by Maddala, G. S. and Rao, C. R., North-Holland, NY. (in press).
18. Mittnik, S. and Rachev, S. T. (1993). Modeling Asset Returns with Alternative Stable Distributions. Econometric Reviews. 12:261-330.
19. Modarres, R., and Nolan, J. P., (1994), "A Method for Simulating Stable Random Vectors", Computational Statistics, 9:11-19.
20. Nolan, J. P. (1997a), "Numerical computation of stable densities and distribution functions", Commun. Statist. - Stochastic Models (to appear).
21. Nolan, J. P. (1997b), "Maximum likelihood estimation of stable parameters", (in preparation).
22. Nolan, J. P. (1997c), "Measures of closeness and dependence for stable distributions", (in preparation).
23. Nolan, J. P., Panorska, A. K. and McCulloch, J. H. (1996) "Estimation of stable spectral measures", (preprint).
24. Nolan, J. P. and Rajput, B., (1995) "Calculation of multidimensional stable densities", Commun. Statist. - Simula., 24:551-556.
25. Panorska, A. K. (1996). Generalized Stable Models for Financial Asset Returns. Journal of Computational and Applied Mathematics, 70, 111-114.
26. Pittel, B., Woyczyński, W. A., and Mann, J. A. (1990), "Random Tree Type Partitions as a Model for Acyclic Polymerization: Holmstark (3/2-stable) distribution of the Supercritical Gel", Ann. Prob., 18:319-341.
27. Plonka, A. and Paszkiewicz, A., (1992), "Kinetics in Dynamically Disordered Systems: Time Scale Dependence of Reaction Patterns in Condensed Media", J. Chem. Phys., 96:1128-1133.
28. Press, S. J. (1972a), "Estimation in Univariate and Multivariate Stable Distributions," JASA, 67:842-846.
29. Press, S. J. (1972b), Applied Multivariate Analysis Holt, Rinehart and Winston, New York.
30. Rachev, S.T., and Samorodnitsky, G., (1993), "Option Pricing Formula for Speculative Prices Modelled by Subordinated Stochastic Processes", Serdica, 19:175-190.
31. Rachev S.T., and Xin, H., (1993), "Test for Association of Random Variables in the Domain of Attraction of Multivariate Stable Law", Probability and Mathematical Statistics, 14 (I) 125-141.
32. Resnick. S. I., and Stǎricǎ, C., (1995), "Smoothing the Hill Estimator", (preprint).
33. Samorodnitsky, G., and Taqqu, M. (1994), Stable Non-Gaussian Random Processes, New York: Chapman and Hall.
34. Scher, H., Schlesinger, M. F., and Bendler, J. T., (1991), "Time-scale Invariance in Transport and Relaxation", Phys. Today, 44, 26-34.
35. Stuck, B. W. (1976) "Distinguishing stable probability measures", Bell System Technical Journal 55:1125-1182.
36. Weron, K., (1991), "A Probabilistic Mechanism Hidden Behind the Universal Power Law for Dielectric Relaxation: General Relaxation Equation", J. Phys.: Condens. Matter, 3, 9151-9162.
37. Weron, K. and Jurlewicz, A., (1993), "Two Forms of Self-similarity as a Fundamental Feature of the Power-law Dielectric Response, J. Phys. A: Math. Gen. 26, 395-410.
38. Weron, A., and Weron, K., (1987), "A Statistical Approach to Relaxation in Glassy Materials", Math. Stat. Prob. Theory, vol B, P. Bower et al (eds.), Reidel, 245-254.