TY - JOUR
T1 - Hypothesis testing for tail dependence parameters on the boundary of the parameter space
AU - Kiriliouk, Anna
N1 - Funding Information:
The author would like to thank two reviewers and an associate editor for their careful reading of the paper and their constructive comments that greatly improved the generality of the paper. She would also like to thank Johan Segers for helpful comments on an earlier version of this paper.
Publisher Copyright:
© 2019 EcoSta Econometrics and Statistics
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/10
Y1 - 2020/10
N2 - Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter space. Hypothesis tests are proposed for tail dependence parameters that, under the null hypothesis, are on the boundary of the alternative hypothesis. The asymptotic distribution of the weighted least squares estimator is given when the true parameter vector is on the boundary of the parameter space, and two test statistics are proposed. The performance of these test statistics is evaluated for the Brown–Resnick model and the max-linear model. In particular, simulations show that it is possible to recover the optimal number of factors for a max-linear model. Finally, the methods are applied to characterize the dependence structure of two major stock market indices, the DAX and the CAC40.
AB - Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter space. Hypothesis tests are proposed for tail dependence parameters that, under the null hypothesis, are on the boundary of the alternative hypothesis. The asymptotic distribution of the weighted least squares estimator is given when the true parameter vector is on the boundary of the parameter space, and two test statistics are proposed. The performance of these test statistics is evaluated for the Brown–Resnick model and the max-linear model. In particular, simulations show that it is possible to recover the optimal number of factors for a max-linear model. Finally, the methods are applied to characterize the dependence structure of two major stock market indices, the DAX and the CAC40.
KW - Brown–Resnick model
KW - Hypothesis testing
KW - Max-linear model
KW - Multivariate extremes
KW - Stable tail dependence function
KW - Tail dependence
UR - http://www.scopus.com/inward/record.url?scp=85070190310&partnerID=8YFLogxK
U2 - 10.1016/j.ecosta.2019.06.001
DO - 10.1016/j.ecosta.2019.06.001
M3 - Article
AN - SCOPUS:85070190310
SN - 2468-0389
VL - 16
SP - 121
EP - 135
JO - Econometrics and Statistics
JF - Econometrics and Statistics
ER -