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Tail dependence of recursive max-linear models with regularly varying noise variables

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  • Gissibl, Nadine
  • Klüppelberg, Claudia
  • Otto, Moritz

Abstract

Recursive max-linear structural equation models with regularly varying noise variables are considered. Their causal structure is represented by a directed acyclic graph (DAG). The problem of identifying a recursive max-linear model and its associated DAG from its matrix of pairwise tail dependence coefficients is discussed. For example, it is shown that if a causal ordering of the associated DAG is additionally known, then the minimum DAG representing the recursive structural equations can be recovered from the tail dependence matrix. For a relevant subclass of recursive max-linear models, identifiability of the associated minimum DAG from the tail dependence matrix and the initial nodes is shown. Algorithms find the associated minimum DAG for the different situations. Furthermore, given a tail dependence matrix, an algorithm outputs all compatible recursive max-linear models and their associated minimum DAGs.

Suggested Citation

  • Gissibl, Nadine & Klüppelberg, Claudia & Otto, Moritz, 2018. "Tail dependence of recursive max-linear models with regularly varying noise variables," Econometrics and Statistics, Elsevier, vol. 6(C), pages 149-167.
    • Handle: RePEc:eee:ecosta:v:6:y:2018:i:c:p:149-167
    DOI: 10.1016/j.ecosta.2018.02.003
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    References listed on IDEAS

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    Cited by:

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    2. Klüppelberg, Claudia & Sönmez, Ercan, 2022. "Max-linear models in random environment," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    3. Kiriliouk, Anna, 2020. "Hypothesis testing for tail dependence parameters on the boundary of the parameter space," Econometrics and Statistics, Elsevier, vol. 16(C), pages 121-135.
    4. Klüppelberg, Claudia & Krali, Mario, 2021. "Estimating an extreme Bayesian network via scalings," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    5. Segers, Johan, 2019. "One- versus multi-component regular variation and extremes of Markov trees," LIDAM Discussion Papers ISBA 2019001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Hu, Shuang & Peng, Zuoxiang & Segers, Johan, 2022. "Modelling multivariate extreme value distributions via Markov trees," LIDAM Discussion Papers ISBA 2022021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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