Geodesic
Extremal (in)dependence of a maximum autoregressive process
Discussiones Mathematicae. Probability and Statistics, Tome 33 (2013) no. 1-2, pp. 47-64.

Voir la notice de l'article provenant de la source Library of Science

Maximum autoregressive processes like MARMA (Davis and Resnick, [5] 1989) or power MARMA (Ferreira and Canto e Castro, [12] 2008) have singular joint distributions, an unrealistic feature in most applications. To overcome this pitfall, absolute continuous versions were presented in Alpuim and Athayde [2] (1990) and Ferreira and Canto e Castro [14] (2010b), respectively. We consider an extended version of absolute continuous maximum autoregressive processes that accommodates both asymptotic tail dependence and independence. A full characterization of the bivariate lag-m tail dependence is presented. This will be useful in an adjustment procedure of the model to real data. An illustration with financial data is presented at the end.
Mots-clés : extreme value theory, autoregressive processes, tail dependence, asymptotic tail independence 
@article{DMPS_2013_33_1-2_a3,
     author = {Ferreira, Marta},
     title = {Extremal (in)dependence of a maximum autoregressive process},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {47--64},
     publisher = {mathdoc},
     volume = {33},
     number = {1-2},
     year = {2013},
     zbl = {1321.60109},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a3/}
}
TY  - JOUR
AU  - Ferreira, Marta
TI  - Extremal (in)dependence of a maximum autoregressive process
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2013
SP  - 47
EP  - 64
VL  - 33
IS  - 1-2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a3/
LA  - en
ID  - DMPS_2013_33_1-2_a3
ER  - 
%0 Journal Article
%A Ferreira, Marta
%T Extremal (in)dependence of a maximum autoregressive process
%J Discussiones Mathematicae. Probability and Statistics
%D 2013
%P 47-64
%V 33
%N 1-2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a3/
%G en
%F DMPS_2013_33_1-2_a3
Ferreira, Marta. Extremal (in)dependence of a maximum autoregressive process. Discussiones Mathematicae. Probability and Statistics, Tome 33 (2013) no. 1-2, pp. 47-64. https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a3/

[1] M.T. Alpuim, An extremal Markovian sequence, J. Appl. Probab. 26 (1989) 219-232. doi: 10.2307/3214030.

[2] M.T. Alpuim and E. Athayde, On the stationary distribution of some extremal Markovian sequences, J. Appl. Probab. 27 (1990) 291-302. doi: 10.2307/3214648.

[3] J. Beirlant, Y. Goegebeur, J. Segers and J. Teugels, Statistics of Extremes: Theory and Application (John Wiley, Chichester, UK, 2004). doi: 10.1002/0470012382.

[4] P. Embrechts, C. Klüppelberg and T. Mikosch, Modelling Extremal Events for Insurance and Finance (Springer-Verlag, Berlin, 1997).

[5] R. Davis and S. Resnick, Basic properties and prediction of max-ARMA processes, Adv. Appl. Probab. 21 (1989) 781-803. doi: 10.2307/1427767.

[6] A.L.M. Dekkers, J.H.J. Einmahl and L. de Haan, A moment estimator for the index of an extreme value distribution, Ann. Statist. 17 (1989) 1833-1855. doi: 10.1214/aos/1176347397.

[7] D. Dietrich, L. de Haan and J. Hüsler, Testing extreme value conditions, Extremes 5 (2000) 71-85. doi: 10.1023/A:1020934126695.

[8] G. Draisma, H. Drees, A. Ferreira and L. de Haan, Bivariate tail estimation: dependence in asymptotic independence, Bernoulli 10 (2004) 251-280. doi: 10.3150/bj/1082380219.

[9] H. Drees, Extreme quantile estimation for dependent data with applications to finance, Bernoulli 9 (2003) 617-657. doi: 10.3150/bj/1066223272.

[10] M. Ferreira, On tail dependence: a characterization for first-order max-autoregressive processes, Math. Notes 90 (2011) 103-114. doi: 10.1134/S0001434611110277.

[11] M. Ferreira, Parameter estimation and dependence characterization of the MAR(1) process, ProbStat Forum 5 (2012) 107-111.

[12] M. Ferreira and L. Canto e Castro, Tail and dependence behaviour of levels that persist for a fixed period of time, Extremes 11 (2008) 113-133. doi: 10.1007/s10687-007-0046-y.

[13] M. Ferreira and L. Canto e Castro, Asymptotic and pre-asymptotic tail behavior of a power max-autoregressive model, ProbStat Forum 3 (2010a) 91-107.

[14] M. Ferreira and L. Canto e Castro, Modeling rare events through a pRARMAX process, J. Statist. Plann. Inference 140 (2010b) 3552-3566. doi: 10.1016/j.jspi.2010.05.024.

[15] M. Ferreira and L. Canto e Castro, A Method For Fitting A pRARMAX Model: An Application To Financial Data, in: Proceedings of The World Congress on Engineering 2010 Vol. III, Lecture Notes in Engineering and Computer Science (Ed(s)), (London, U.K., 2010c) 2022-2026.

[16] G. Frahm, M. Junker and R. Schmidt, Estimating the tail-dependence coefficient: properties and pitfalls, Insurance Math. Econom. 37 (2005) 80-100. doi: 10.1016/j.insmatheco.2005.05.008.

[17] J.E. Heffernan, J.A. Tawn and Z. Zhang, Asymptotically (in)dependent multivariate maxima of moving maxima processes, Extremes 10 (2007) 57-82. doi: 10.1007/s10687-007-0035-1.

[18] B.M. Hill, A simple general approach to inference about the tail of a distribution, Ann. Statist. 3 (1975) 1163-1174. doi: 10.1214/aos/1176343247.

[19] A.V. Lebedev, Statistical analysis of first-order MARMA processes, Math. Notes 83 (2008) 506-511. doi: 10.1134/S0001434608030243.

[20] Z. Zhang, A New Class of Tail-Dependent Time Series Models and Its Applications in Financial Time Series, Advances in Econometrics 20B (2005) 323-358.