dc.description |
1. Podobnik, B., Valentinčič, A., Horvatić, D., Stanley, H.E.: Asymmetric Lévy flight in
financial ratios. Proceedings of the National Academy of Sciences of the United States of
America. 108(44), 17883–17888 (2011). doi:10.1073/pnas.1113330108
2. Baruník, J., Vácha, L., Vošvrda, M.: Tail behavior of the Central European stock markets
during the financial crisis. AUCO Czech Economic Review. 4(3), 281–295 (2010)
3. Bachelier, L.: Théorie de la spéculation. Annales scientifiques de l'École Normale
Supérieure, Série 3. 17, 21–86 (1900). doi:10.24033/asens.476
4. Gopikrishnan, P., Plerou, V., Amaral, L.A.N., Meyer, M., Stanley, H.E.: Scaling of the
distribution of fluctuations of financial market indices. Physical Review E - Statistical
Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 60(3), 5305–5316 (1999).
doi:10.1103/PhysRevE.60.5305
5. Gabaix, X., Gopikrishnan, P., Plerou, V., Stanley, H.E.: A Theory of Power Law
Distributions in Financial Market Fluctuations. Nature. 423(6937), 267–270 (2003)
6. Gabaix, X., Gopikrishnan, P., Plerou, V., Stanley, H.E.: Institutional Investors and Stock
Market Volatility. Quarterly Journal of Economics. 121(2), 461–504 (2006).
doi:10.3386/w11722
7. Mandelbrot, B.: The variation of certain speculative prices. The Journal of Business. 36(4),
394–419 (1963). doi:10.1086/294632
8. Levy, P.: Théorie des erreurs. La loi de Gauss et les lois exceptionnelles. Bulletin de la
Société Mathématique de France. 52, 49–85 (1924)
9. Gnedenko, B.V., Kolmogorov, A.N.: Limit Distributions for Sums of Independent Random
Variables. Addison-Wesley, Cambridge (1954) 10. Fama, E.F.: The Behavior of Stock-Market Prices. The Journal of Business. 38(1), 34–105
(1965).
11. Mantegna, R.N., Stanley, H.E.: Scaling behaviour in the dynamics of an economic index.
Nature. 376, 46–49 (1995).
12. Weron, R.: Levy-stable distributions revisited: tail index > 2 does not exclude the Levystable regime. International Journal of Modern Physics C. 12(2), 209–223 (2001).
13. Koutrouvelis, I.A.: Regression-Type Estimation of the Parameters of Stable Laws. Journal
of the American Statistical Association. 75(372), 918–928 (1980)
14. Brorsen, B.W., Yang, S.R.: Maximum Likelihood Estimates of Symmetric Stable
Distribution Parameters. Communications in Statistics - Simulation and Computation. 19(4),
1459–1464 (1990). doi:10.1080/03610919008812928
15. Nolan, J.P.: Maximum likelihood estimation of stable parameters. In: Barndorff-Nielsen,
O.E., Mikosch, T., Resnick, S.I. (eds.) Lévy Processes: Theory and Applications, pp. 379–
400. Springer Science+Business Media, Boston (2001)
16. Fama, E.F., Roll, R.: Parameter estimates for symmetric stable distributions. Journal of the
American Statistical Association. 66(334), 331–338 (1971). doi:10.2307/2283932
17. McCulloch, J.H.: Simple consistent estimators of stable distribution parameters.
Communications in Statistics - Simulation and Computation. 15(4), 1109–1136 (1986)
18. Shao, M., Nikias, C. L.: Signal processing with fractional lower order moments: stable
processes and their application. Proceedings of the IEEE. 81(7), 986–1010 (1993). doi:
10.1109/5.231338
19. Ma, X., Nikias, C.L.: Joint estimation of time delay and frequency delay in impulsive noise
using fractional lower order statistics. IEEE Transactions on Signal Processing. 43(11),
2669–2687 (1996). doi:10.1109/78.542175
20. Nicolas, J.-M., Anfinsen, S. N.: Introduction to second kind statistics: Application of logmoments and log-cumulants to the analysis of radar image distributions. Traitement du
Signal. 19(3), 139–167 (2002)
21. Kuruoğlu, E.E.: Density parameter estimation of skewed α-stable distributions. IEEE
Transactions on Signal Processing. 49(10), 2192–2201 (2001). doi:10.1109/78.950775
22. DuMouchel, W.H.: On the Asymptotic Normality of the Maximum Likelihood Estimate
When Sampling from a Stable Distribution. The Annals of Statistics 1(5), 948–957 (1973)
23. Zolotarev, V.M.: One-dimensional Stable Distributions. American Mathematical Society,
Providence (1986)
24. Chambers, J.M., Mallows, C.L., Stuck, B.W.: A Method for Simulating Stable Random
Variables: Journal of the American Statistical Association. 71(354), 340–344 (1976).
25. Koutrouvelis, I.A.: An iterative procedure for the estimation of the parameters of stable laws:
An iterative procedure for the estimation. Communications in Statistics - Simulation and
Computation. 10(1), 17–28 (1981). doi:10.1080/03610918108812189
26. Arnold, V.I., Avez, A.: Ergodic problems of classical mechanics. Benjamin, New York
(1968). doi:zamm.19700500721
27. Umeno, K.: Ergodic transformations on R preserving Cauchy laws. Nonlinear Theory and
Its Applications. 7(1), 14–20 (2016). doi:10.1587/nolta.7.14
28. Charles, A., Darné, O.: Large shocks in the volatility of the Dow Jones Industrial Average
index: 1928–2013. Journal of Banking & Finance. 43(C), 188–199 (2014).
doi:10.1016/j.jbankfin.2014.03.022
29. Duarte, F.B., Tenreiro Machado, J.A., Monteiro Duarte, G.: Dynamics of the Dow Jones and
the NASDAQ stock indexes. Nonlinear Dynamics. 61(4), 691–705 (2010).
doi:10.1007/s11071-010-9680-z 30. Soloviev, V.M., Chabanenko, D.M.: Dynamika parametriv modeli Levi dlia rozpodilu
prybutkovostei chasovykh riadiv svitovykh fondovykh indeksiv (Dynamics of parameters
of the Levy model for distribution of profitability of time series of world stock indexes). In:
Pankratova, E.D. (ed.) Proceedings of 16-th International Conference on System Analysis
and Information Technologies (SAIT 2014), Kyiv, Ukraine, May 26-30, 2014. ESC “IASA”
NTUU “KPI”, Kyiv (2014)
31. Soloviev, V., Solovieva, V., Chabanenko, D.: Dynamics of α-stable Levi process parameters
for returns distribution of the financial time series. In: Chernyak, O.I., Zakharchenko, P.V.
(eds.) Contemporary concepts of forecasting the development of complex socio-economic
systems, pp. 257–264. FO-P Tkachuk O.V, Berdyansk (2014)
32. Fukunaga, T., Umeno, K.: Universal Lévy's stable law of stock market and its
characterization. https://arxiv.org/pdf/1709.06279 (2018). Accessed 21 Mar 2019
33. Bielinskyi, A., Semerikov, S., Solovieva, V., Soloviev, V.: Levy’s stable distribution for
stock crash detecting. SHS Web of Conferences. 65, 06006 (2019).
doi:10.1051/shsconf/20196506006 |
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