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Friday, January 12, 2018

Friday, January 12, 2018 — 1:30 PM EST

Testing the multivariate regular variation model for extreme risks

Heavy-tail phenomena generally exist in insurance, finance and economics. Multivariate regular variation (MRV) is one of the most important structures in modeling multivariate extreme risks with heavy-tailed marginal distributions and flexible dependence structures. In this paper, we propose a formal goodness-of-fit test for the MRV model. The test is based on comparing the tail indices of the radial component conditional on the angular component falling in different subsets. We first establish the estimator of the conditional tail index and prove the joint asymptotic property for all such estimators. We further combine the test on the constancy across different conditional tail indices with testing the regular variation of the radial component. Our proofs are based on the asymptotic properties of tail and non-tail empirical processes. Simulation studies demonstrate the good performance of the proposed tests, and real market data applications are also provided.

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