| The larger part of the team is located at the Chair for
Applied Mathematical
Statistics in the Department of Mathematics, whereas the remaining
researchers work at the Fraunhofer institute ITWM in the
departments Financial Mathematics,
Mathematical Methods for Dynamics and Durability und Models and Algorithms of Image Processing.
The research of the group is centered around the development of models
and statistical estimation and testing procedures for nonlinear time
series and spatial stochastic processes. Current focusses of
applications are financial time series analysis, risk management and
image processing. The main types of models and methods under
investigation are:
Models:
-
nonparametric, discrete-time versions of the model underlying the Black-Scholes
aproach to derivative pricing, i.e. nonlinear, nonparametric
heteroscedastic autoregressions and more general stochastic volatility
models
-
ARCH- and GARCH-processes and nonparametric generalizations
-
nonparametric models for multivariate time series based on neural networks
-
nonstationary time series with slowly changing structure, e.g. autoregressions with slowly varying coefficients
-
locally-stationary time series or spatial
processes with abrupt structural breaks (changepoints), e.g.
autoregressions with constant coefficients between the random
changepoints
Methods:
-
nonparametric local and global smoothers (kernel estimates, local polynomials etc.) or wavelet-based function estimates
-
Bootstrap-approximations for distributions of estimated time series parameters, e.g. conditional expectations or quantiles
- methods for detecting changepoints in time series
- extrem value theory for time series with applications in risk management
|
