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Detecting Tail Risk Differences in Multivariate Time Series
Author(s) -
Hoga Yannick
Publication year - 2018
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12292
Subject(s) - multivariate statistics , mathematics , extreme value theory , econometrics , statistics , series (stratigraphy) , normalization (sociology) , tail risk , expected shortfall , limit (mathematics) , value at risk , multivariate analysis , risk management , economics , sociology , anthropology , biology , paleontology , mathematical analysis , management
We derive functional central limit theory for tail index estimates in multivariate time series under mild conditions on the extremal dependence between the components. We use this result to also derive convergence results for extreme value‐at‐risk and extreme expected shortfall estimates. This allows us to construct tests for equality of ‘tail risk’ in multivariate data, which can be useful in a number of empirical contexts. In constructing test statistics, we avoid estimating long‐run variances by using self‐normalization. Size and power of the tests for equal ‘tail risk’ are assessed in simulations. An empirical application to exchange returns illustrates the practical usefulness of the tests.