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Illia Horenko, Free University of Berlin Print
Friday, 09 October 2009, 14:30 - 15:30

Computational Time Series Analysis of Multidimensional Non-Stationary Data

Abstract: In recent years there has been considerable increase of interest in the mathematical modeling and computational analysis of complex non-stationary and non-equilibrium systems. Such systems can be found, e.g., in weather forecast (transitions between weather conditions), climate research (processes associated with global warming), fluid mechanics (transient processes between different flow regimes and interfaces) and in econometrics (e.g., switches between phases of different market dynamics). In all cases the accumulation of suffciently detailed multidimensional time series has led to the formation of huge databases containing enormous but still undiscovered treasures of information. However, the extraction of essential information out of the data is usually hindered by the multidimensional and non-stationary nature of the signal. The standard filtering approaches have in general unfeasible numerical complexity in high dimensions, other standard methods (like f. e. Kalman-filter,MVAR, ARCH/GARCH etc.) impose some too restrictive statistical assumptions about the type of the underlying dynamics. A new method for analysis of multidimensional non-stationary time series will be presented (I. Horenko (2008)). The approach is based on optimization of the averaged clustering functional in appropriate function spaces. Considered functional describes the quality of data representation in terms of several optimally localized models and a persistent process switching between the models.  Resulting computational framework is based on application of the nite element method (FEM) to the variational minimization of the introduced functional in different functional spaces. The computational advantages of the presented method will be discussed in comparison to the standard stochastic approaches (like Hidden Markov Models (HMMs)) and statistical aspects of the data post-processing will be discussed. The application of the computational framework will be brie y demonstrated in context of reduced data-based climate models, models of optimal future portfolios in computational nance and reduced representation of molecular dynamics in computational biophysics.

Illia Horenko, Free University of Berlin

Location: Campus Plaine 2NO906
Contact: Jacqueline Douilly, This e-mail address is being protected from spam bots, you need JavaScript enabled to view it