The next EVTA seminars will take place in Room HG-05A16, Main Building, Vrije Universiteit Amsterdam.
Address: De Boelelaan 1105, 1081 HV Amsterdam.
Title: Simulation of extreme values with neural networks
Abstract: Neural networks based on Rectified linear units (ReLU) cannot efficiently approximate quantile functions which are not bounded, especially in the case of heavy-tailed distributions. We thus propose a new parametrization for the generator of a generative adversarial network (GAN) adapted to this framework, basing on extreme-value theory. An analysis of the uniform error between the extreme quantile and its GAN approximation is provided: We establish that the rate of convergence of the error is mainly driven by the second-order parameter of the data distribution. The above results are illustrated on simulated data and real financial data. It appears that our approach outperforms the classical GAN in a wide range of situations including high-dimensional and dependent data.
This is joint work with Michaël Allouche and Emmanuel Gobet (Ecole Polytechnique, France).
Title: : Detecting structural changes in the tail-index of long memory stochastic volatility time series
Abstract: We consider a change-point test based on the Hill estimator to test for structural changes in the tail index of long-memory stochastic volatility (LMSV) time series. In order to determine the asymptotic distribution of the corresponding test statistic, we prove a uniform reduction principle for the tail empirical process in a two-parameter Skorohod space. It is shown that such a process displays a dichotomous behavior according to an interplay between the Hurst parameter, i.e. a parameter characterizing the dependence in the data, and the tail index. We will see that, nonetheless, long-memory does not have an influence on the asymptotic behavior of the test statistic.