On the tail index estimation of an autoregressive Pareto process
Discussiones Mathematicae Probability and Statistics, Tome 33 (2013) no. 1-2, p. 65.

Voir la notice de l'article dans European Digital Mathematics Library

In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision.
Classification : 60G15, 60G70, 62G32
Mots-clés : extreme value theory, autoregressive processes, tail index estimation, autoregressive Pareto process, Gaussian process 
@article{DMPS_2013__33_1-2_270855,
     author = {Marta Ferreira},
     title = {On the tail index estimation of an autoregressive {Pareto} process},
     journal = {Discussiones Mathematicae Probability and Statistics},
     pages = {65},
     publisher = {mathdoc},
     volume = {33},
     number = {1-2},
     year = {2013},
     zbl = {1319.60114},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DMPS_2013__33_1-2_270855/}
}
TY  - JOUR
AU  - Marta Ferreira
TI  - On the tail index estimation of an autoregressive Pareto process
JO  - Discussiones Mathematicae Probability and Statistics
PY  - 2013
SP  - 65
VL  - 33
IS  - 1-2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DMPS_2013__33_1-2_270855/
LA  - en
ID  - DMPS_2013__33_1-2_270855
ER  - 
%0 Journal Article
%A Marta Ferreira
%T On the tail index estimation of an autoregressive Pareto process
%J Discussiones Mathematicae Probability and Statistics
%D 2013
%P 65
%V 33
%N 1-2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DMPS_2013__33_1-2_270855/
%G en
%F DMPS_2013__33_1-2_270855
Marta Ferreira. On the tail index estimation of an autoregressive Pareto process. Discussiones Mathematicae Probability and Statistics, Tome 33 (2013) no. 1-2, p. 65. https://geodesic-test.mathdoc.fr/item/DMPS_2013__33_1-2_270855/