Abstract
Financial data (log-returns of exchange rates, stock indices, share prices) are often modeled by heavy-tailed distributions, i.e., distributions which admit the representation
where the function L slowly varies: \(\mathop {\lim }\limits_{x \to \infty } L(xt)/L(x) = 1(\forall t > 0)\).
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Bibliography
Bradley, R. (1986). Basic properties of strong mixing condition, in E. Eberlein and M.S. Taqqu (eds), Dependence in Probability and Statistics, Boston: Birkhäuser, pp. 165–192.
Csörgö, S. and Viharos, L. (1998). Asymptotic Methods in Probability and Statistics, Elsevier, chapter Estimating the tail index, pp. 833–881.
Davis, R., Mikosch, T. and Basrak, B. (1999). Sample acf of multivariate stochastic recurrence equations with applications to garch, Technical report, University of Groningen, Department of Mathematics.
de Haan, L. and Peng, L. (1998). Comparison of tail index estimators, Statistica Neerlandica 52(1): 60–70.
Drees, H. (1999). Weighted approximations of tail processes under mixing conditions, Technical report, University of Cologne.
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer Verlag.
Hsing, T. (1991). On tail index estimation for dependent data, 19(3): 1547–1569.
Novak, S. (1996). On the distribution of the ratio of sums of random variables, Theory Probab. Appl. 41(3): 479–503.
Novak, S. (1998). Berry-esseen inequalities for a ratio of sums of random variables, Technical Report 98, University of Sussex.
Novak, S. and Utev, S. (1990). On the asymptotic distribution of the ratio of sums of random variables, Siberian Math. J. 31: 781–788.
Resnick, S. (1997). Heavy tail modeling and teletraffic data, Ann. Statist. 25(5): 1805–1869.
Resnick, S. and Starica, C. (1998). Tail index estimation for dependent data, Ann. Appl. Probab. 8(4): 1156–1183.
Utev, S. (1989). Sums of ϕ-mixing random variables, Technical report, Trudy Inst. Mat. (Novosibirsk).
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Novak, S.Y. (2000). Confidence intervals for a tail index estimator. In: Franke, J., Stahl, G., Härdle, W. (eds) Measuring Risk in Complex Stochastic Systems. Lecture Notes in Statistics, vol 147. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1214-0_14
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DOI: https://doi.org/10.1007/978-1-4612-1214-0_14
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