Geodesic
Fitting time series with heavy tails and strong time dependence
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 3, pp. 127-144.

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Earlier, a model of a time series with heavy tails constructed from a Gaussian time series was developed. In the present paper, the reverse problem is considered: an estimator of the copula function is built; the copula function is a nonlinear function that maps Gaussian variables to the variables from Fréchet maximum domain of attraction. The statistical properties of this estimator are considered for a stationary time series with a low rate of covariance decay. 
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A. E. Mazur. Fitting time series with heavy tails and strong time dependence. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 3, pp. 127-144. http://geodesic.mathdoc.fr/item/FPM_2018_22_3_a7/

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

[2] Mazur A. E., Piterbarg V. I., “Gaussovskie kopulnye vremennye ryady s tyazhelymi khvostami i silnoi vremennoi zavisimostyu”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 70:5 (2015), 197–201 | Zbl

[3] Piterbarg V. I., Dvadtsat lektsii o gaussovskikh protsessakh, MTsNMO, M., 2015

[4] Drees H., “A general class of estimators of the extreme value index”, J. Statist. Planning Inference, 66:1 (1998), 95–112 | DOI | MR | Zbl

[5] Drees H., “On smooth statistical tail functionals”, Scand. J. Statist., 25:1 (1998), 187–210 | DOI | MR | Zbl

[6] Drees H., “Weighted approximation of tail processes for $\beta$-mixing random variables”, Ann. Appl. Probab., 10:4 (2000), 1274–1301 | MR | Zbl

[7] Drees H., “Tail empirical processes under mixing conditions”, Empirical Process Techniques for Dependent Data, eds. Dehling H., Mikosch T., Sørensen M., Birkhäuser, Boston, 2002, 325–342 | DOI | MR | Zbl

[8] Gill R. D., “Non- and semi-parametric maximum likelihood estimators and the von Mises method (part 1)”, Scand. J. Statist., 16:2 (1989), 97–128 | MR | Zbl

[9] De Haan L., Ferreira A., Extreme Value Theory: An Introduction, Springer, New York, 2007 | MR

[10] Hill B. M., “A simple general approach to inference about the tail of a distribution”, Ann. Statist., 3:5 (1975), 1163–1174 | DOI | MR | Zbl

[11] Piterbarg V. I., Asymptotic Methods in Theory of Gaussian Random Processes and Fields, Transl. Math. Monogr., 148, Amer. Math. Soc., Providence, 2012 | DOI | MR

[12] Rootzén H., “Weak convergence of the tail empirical process for dependent sequences”, Stoch. Processes Their Appl., 119:2 (2009), 468–490 | DOI | MR | Zbl