Statistical Inference on Sets, Nonparametric Financial Time Series and Extreme Value theory

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The project consists in two parts: statistical inference on sets and nonparametric financial time series. The first topic is confidence regions for nonparametric sets. The construction is based on nonparametric curve estimators. Mathematically, this requires the analysis of the distribution of suprema of smoothing estimators over manifolds. Sets of interest are e.g. level sets of curves, ridges, intersections of curves, and intersection bounds. Such sets arise from different fields of applications. The second topic is the construction of GARCH-like financial time series where the dynamics runs over a stochastic recurrence equation but where instead of conditional variances also other conditional nonparametric functionals enter into the model. Extreme value statistics is used to analyse the tail behaviour of the resulting time series and of other already studied GARCH-processes.