Modelling Dependence within Joint Tail Regions

Anthony W. Ledford · Jonathan A. Tawn

424 citations0/0 files storedJournal of the Royal Statistical Society Series B (Statistical Methodology)

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Probability and Risk Models Statistical Distribution Estimation and Applications Financial Risk and Volatility Modeling

Abstract

Summary Standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max-stability, a particular form of joint tail dependence. We develop joint tail models based on a broader class of dependence structure which provides a natural link between max-stable models and weaker forms of dependence including independence and negative association. This approach overcomes many of the problems that are encountered with standard methods and is the basis for a Poisson process representation that generalizes existing bivariate results. We apply the new techniques to simulated and environmental data, and demonstrate the marked advantage that the new approach offers for joint tail extrapolation.

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References

1987Extreme Values, Regular Variation and Point Processes 1990Models for Exceedances Over High Thresholds 1996Statistics for near independence in multivariate extreme values 1989Extreme Value Analysis of Environmental Time Series: An Application to Trend Detection in Ground-Level Ozone 1988Bivariate Extreme Value Theory: Models and Estimation 1991Modelling Extreme Multivariate Events

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