The project is centered on the development of structural adaptive methods for various problems of statistical data analysis with applications to market risk evaluation. We especially focus on methods for the following questions.
Effective dimension reduction of high dimensional datasets: Many problems of financial engineering and econometrics lead to a statistical analysis of high dimensional data. Parametric (linear) models are not sufficiently flexible to describe such data while fully nonparametric models meet the so-called curse of dimensionality problem. Semiparametric models, e.g. single-, multi-index or partial linear models provide a good compromise between too restrictive linear models and too flexible nonparametric models allowing to project the high dimensional data into a low dimensional subspace without significant loss of information. Interest is typically in describing this low dimensional index space.
Modeling of nonstationary time series: Classical time series models assume stationarity of the underlying process. Especially for long financial time series now available from data repositories, e.g. on-line price-processes of stocks or exchange rates, this assumption is questionable. Nonstationarity may be explained by both external shocks and gradual changes of general economic conditions. Natural generalizations of the stationary model are local stationary or local homogeneous time series. In this context we plan to develop structural adaptive methods for modeling and estimation of time inhomogeneous models.