Extremal (in)dependence of a maximum autoregressive process

Marta Ferreira

Discussiones Mathematicae Probability and Statistics (2013)

  • Volume: 33, Issue: 1-2, page 47-64
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Marta Ferreira. "Extremal (in)dependence of a maximum autoregressive process." Discussiones Mathematicae Probability and Statistics 33.1-2 (2013): 47-64. <http://eudml.org/doc/270885>.

@article{MartaFerreira2013,
abstract = {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.},
author = {Marta Ferreira},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {extreme value theory; autoregressive processes; tail dependence; asymptotic tail independence; maximum autoregressive processes},
language = {eng},
number = {1-2},
pages = {47-64},
title = {Extremal (in)dependence of a maximum autoregressive process},
url = {http://eudml.org/doc/270885},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Marta Ferreira
TI - Extremal (in)dependence of a maximum autoregressive process
JO - Discussiones Mathematicae Probability and Statistics
PY - 2013
VL - 33
IS - 1-2
SP - 47
EP - 64
AB - 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.
LA - eng
KW - extreme value theory; autoregressive processes; tail dependence; asymptotic tail independence; maximum autoregressive processes
UR - http://eudml.org/doc/270885
ER -

References

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