Location: Room K1203
Title: Directed graphical models and structural causal models in multivariate extremes from threshold exceedances
Abstract: The recent introduction of conditional independence in multivariate extremes from threshold exceedances opened many new research directions in extremal dependence modeling. In particular, many papers have considered undirected graphical models based on this new notion of extremal conditional independence. In this talk we introduce directed graphical models based on extremal conditional independence, and discuss the resulting directed extremal Markov properties as well as Markov equivalence. Furthermore, we introduce a limiting extremal SCM that conforms with our directed extremal Markov properties. For the parametric subclass of Hüsler–Reiss distributions, we find a simple linear extremal SCM that permits a parametric description of extremal conditional independence. This gives rise to an extremal conditional independence test, which we implement in a PC-type algorithm. Finally, we demonstrate our approach on real data.
This is joint work with Sebastian Engelke and Nicola Gnecco.
Location: Room K1206
Title: Extremal regression in heavy-tailed models
Abstract: Studying rare events at the heavy tails of Pareto-type distributions, in the presence of high-dimensional covariates, is a burgeoning science and has many applications both in and out of finance. Most attempts to tackle the subject involve quantile regression, which usually offers a natural way of examining the impact of covariates at different levels of the dependent variable. In risk management, however, quantiles are often criticized for their failure to be subadditive in general, and for their lack of sensitivity to the magnitude of extreme losses. This bolstered the interest in their least squares analogs, coined as expectiles, which define the only coherent law-invariant risk measure that is also elicitable, namely, they benefit from a straightforward backtesting methodology. For the estimation of both extreme conditional quantiles and expectiles, we develop a general theory using a flexible tail location-scale quantile regression model with heavy-tailed noise. We introduce versatile residual-based estimators of extremal regression quantiles and expectiles and derive their asymptotic properties in a general setting. We then tailor the discussion to the linear and local linear estimation settings. We showcase the performance of our procedures in a detailed simulation study and apply them to concrete financial data.