A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions

John Einmahl, A. Kiriliouk, J.J.J. Segers

Research output: Working paperDiscussion paperOther research output

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Abstract

Likelihood-based procedures are a common way to estimate tail dependence parameters.They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to compute in higher dimensions. An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator. The estimator is easy to calculate and applies to a wide range of sampling schemes and tail dependence models. In large samples, it is asymptotically normal with an explicit and estimable covariance matrix. The minimum distance obtained forms the basis of
a goodness-of-t statistic whose asymptotic distribution is chi-square. Extensive Monte Carlo simulations confirm the excellent finite-sample performance of the estimator and demonstrate that it is a strong competitor to currently available methods. The estimator is then applied to disentangle sources of tail dependence in European stock markets.
Original languageEnglish
Place of PublicationTIlburg
PublisherCentER, Center for Economic Research
Number of pages24
Volume2016-002
Publication statusPublished - 18 Jan 2016

Publication series

NameCentER Discussion Paper
Volume2016-002

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Weighted Least Squares Estimator
Tail Dependence
Higher Dimensions
Updating
Estimator
Minimum Distance Estimator
Dependence Function
Structural Equation Model
Chi-square
Weighted Least Squares
Minimum Distance
Stock Market
Estimate
Asymptotic distribution
Covariance matrix
Statistic
Linear equation
Likelihood
Monte Carlo Simulation
Calculate

Keywords

  • Brown-resnick process
  • extremal coefficient
  • max-linear model
  • multivariate extremes
  • stable tail dependence function

Cite this

Einmahl, J., Kiriliouk, A., & Segers, J. J. J. (2016). A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions. (CentER Discussion Paper; Vol. 2016-002). TIlburg: CentER, Center for Economic Research.
Einmahl, John ; Kiriliouk, A. ; Segers, J.J.J. / A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions. TIlburg : CentER, Center for Economic Research, 2016. (CentER Discussion Paper).
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Einmahl, J, Kiriliouk, A & Segers, JJJ 2016 'A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions' CentER Discussion Paper, vol. 2016-002, CentER, Center for Economic Research, TIlburg.

A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions. / Einmahl, John; Kiriliouk, A.; Segers, J.J.J.

TIlburg : CentER, Center for Economic Research, 2016. (CentER Discussion Paper; Vol. 2016-002).

Research output: Working paperDiscussion paperOther research output

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N2 - Likelihood-based procedures are a common way to estimate tail dependence parameters.They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to compute in higher dimensions. An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator. The estimator is easy to calculate and applies to a wide range of sampling schemes and tail dependence models. In large samples, it is asymptotically normal with an explicit and estimable covariance matrix. The minimum distance obtained forms the basis ofa goodness-of-t statistic whose asymptotic distribution is chi-square. Extensive Monte Carlo simulations confirm the excellent finite-sample performance of the estimator and demonstrate that it is a strong competitor to currently available methods. The estimator is then applied to disentangle sources of tail dependence in European stock markets.

AB - Likelihood-based procedures are a common way to estimate tail dependence parameters.They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to compute in higher dimensions. An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator. The estimator is easy to calculate and applies to a wide range of sampling schemes and tail dependence models. In large samples, it is asymptotically normal with an explicit and estimable covariance matrix. The minimum distance obtained forms the basis ofa goodness-of-t statistic whose asymptotic distribution is chi-square. Extensive Monte Carlo simulations confirm the excellent finite-sample performance of the estimator and demonstrate that it is a strong competitor to currently available methods. The estimator is then applied to disentangle sources of tail dependence in European stock markets.

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KW - max-linear model

KW - multivariate extremes

KW - stable tail dependence function

M3 - Discussion paper

VL - 2016-002

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Einmahl J, Kiriliouk A, Segers JJJ. A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions. TIlburg: CentER, Center for Economic Research. 2016 Jan 18. (CentER Discussion Paper).