# Extremal (in)dependence of a maximum autoregressive process

Discussiones Mathematicae Probability and Statistics (2013)

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

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topMarta 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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