Geodesic
Gaussian copula time series with heavy tails and strong time dependence
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2015), pp. 3-7 Cet article a éte moissonné depuis la source Math-Net.Ru

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A class of functions $f$ is described for which the random variable $X=f(\xi)$, where $\xi$ is a standard normal random variable, belongs to Fréchet maximum domain of attraction. For any $f$ from this class, a limit theorem for the maximum of the sequence $X(k)=f(\xi_{k})$, $k=1,2,\dots$, is proved, where $\xi_{k}$ is a Gaussian stationary sequence with a slowly decreasing correlation. 
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A. E. Mazur; V. I. Piterbarg. Gaussian copula time series with heavy tails and strong time dependence. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2015), pp. 3-7. http://geodesic.mathdoc.fr/item/VMUMM_2015_5_a0/

[1] Embrechts P., Kluppelberg C., Mikosch T., Modeling extremal events: for insurance and finance, Springer, Berlin, 1997 | MR

[2] Cont R., “Long range dependence in financial time series”, Fractals in engineering, eds. E. Lutton, J. Lévy-Véhel, Springer, L., 2005, 159–179 | DOI | Zbl

[3] Resnick S.I., “Heavy tail modeling and teletraffic data: special invited paper”, Ann. Statist., 25:5 (1997), 1805–1869 | DOI | MR | Zbl

[4] Mikosch T., “Modeling dependence and tails of financial time series”, Extreme values in finance, telecommunications, and the environment, eds. B. Finkenstädt, H. Rootzén, Chapman and Hall/CRC, Boca Raton, 2004, 196–297 | MR

[5] Heath D., Resnick S., Samorodnitsky G., “Heavy tails and long range dependence in on/off processes and associated fluid model”, Math. Oper. Res., 23:1 (1998), 145–165 | DOI | MR | Zbl

[6] Cherny A.S., Douady R., Molchanov S.A., On measuring hedge fund isk, , 2008 http://ssrn.com/abstract=1113620

[7] Piterbarg V.I., Asymptotic methods in the theory of Gaussian processes and fields, AMS Transl. Math. Monogr., 148, Providence, Rhode Island, 1996 | MR | Zbl

[8] Lidbetter M. R., Lindgren G., Rotsen X., Ekstremumy sluchainykh posledovatelnostei i protsessov, Mir, M., 1989 | MR