Hypothesis testing for tail dependence parameters on the boundary of the parameter space

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    Abstract

    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.

    Original languageEnglish
    Pages (from-to)121-135
    Number of pages15
    JournalEconometrics and Statistics
    Volume16
    DOIs
    Publication statusPublished - Oct 2020

    Keywords

    • Brown–Resnick model
    • Hypothesis testing
    • Max-linear model
    • Multivariate extremes
    • Stable tail dependence function
    • Tail dependence

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