Multivariate Time Series Analysis

In many applications multivariate time series and point processes are recorded. Examinations of interrelations between processes generating these time series are one major challenge in real-world applications and fake data. To get reliable information about the interactions of the recorded time series and point processes bivariate analysis techniques are not sufficient.

Aim of the project

We develop, investigate and assess analysis techniques which allow for detection of relationships between time series and point processes. In most applications the toplogy of the network of processes under consideration is completely unknown. Therefore, it is of particular importance to evaluate not only the sensitivity but also the specifity of the methods; the pros and cons need to be known.

The Team

Prof. Dr. Jens Timmer (Freiburg Center for Data Analysis and Modeling, Freiburg, Germany)

Dr. Björn Schelter, (Freiburg Center for Data Analysis and Modeling, Freiburg, Germany)

Linda Sommerlade, (Freiburg Center for Data Analysis and Modeling, Freiburg, Germany)

Ariane Schad, (Freiburg Center for Data Analysis and Modeling, Freiburg, Germany)

Dr. Katharina Virnich, (Freiburg Center for Data Analysis and Modeling, Freiburg, Germany)

Wolfgang Mader, (Freiburg Center for Data Analysis and Modeling, Freiburg, Germany)

David Feess, (Freiburg Center for Data Analysis and Modeling, Freiburg, Germany)

Olga Lapp, (Freiburg Center for Data Analysis and Modeling, Freiburg, Germany)

Malenka Killmann, (Freiburg Center for Data Analysis and Modeling, Freiburg, Germany)

Books

Schelter B., Winterhalder M., Timmer J. Handbook of Time Series Analysis: Recent Theoretical Developments and Applications ISBN 3-527-40623-9 Wiley-VCH, Berlin

Publications in Reviewed Journals

[17] Jachan M., Henschel K., Nawrath J., Schad A., Timmer J., Schelter B. Inferring direct directed information flow from multivariate non-linear time series. Physical Review E , 2009

[16] Sommerlade L., Henschel K., Wohlmuth J., Jachan M., Amtage F., Hellwig B., Lücking C.H., Timmer J., Schelter B. Time-variant estimation of directed influence during Parkinsonian tremor. Cardiovascular Engineering , 2009

[15] Jachan M., Reinhard M., Spindeler L., Hetzel A., Schelter B., Timmer J. Parametric versus nonparametric transfer function estimation of cerebral autoregulation from spontaneous blood-pressure oscillations. J. Physiol. , 2009

[14] Schelter B., Timmer J., Eichler M. Assessing the strength of directed influences among neural signals using renormalized partial directed coherence J. Neuroscience Methods 179, 2009, 121-130

[13] Mader W., Feess D., Lange R., Saur D., Glauche V., Weiller C., Timmer J., and Schelter B. On the detection of direct directed information flow in fMRI. IEEE J. Selected Topics In Signal Processing 2, 2008, 965-974

[12] Henschel K., Hellwig B., Amtage F., Jachan M., Lücking C.H., Timmer J., Schelter B. Multivariate Analyis of dynamical processes: Point processes and time series. Europ. Phys. J. 165, 2008, 25-34

[11] Winterhalder M., Schelter B., Timmer J. Detecting coupling directions in multivariate oscillatory systems. Int. J. Bif. Chaos 17, 2007, 3725-3739

[10] Schelter B., Winterhalder M., Kurths J., Timmer J. Phase synchronization and coherence analysis: Sensitivity and specificity. Int. J. Bif. Chaos 17, 2007, 3551-3556

[9] Schelter B., Peifer M., Winterhalder M., Timmer J. Testing for phase synchronization. Phys. Lett. A 366, 2007, 382-390

[8] Smirnov D., Schelter B., Winterhalder M., Timmer J. Revealing direction of coupling between neuronal oscillators from time series: Phase dynamics modeling versus partial directed coherence. Chaos 17, 2007, 013111

[7] Winterhalder M., Schelter B., Hesse W., Schwab K., Leistritz L., Timmer J. and Witte H. Detection of directed information flow in multidimensional biosignals. Biomed. Tech. 51, 2006, 281-287

[6] Winterhalder M., Schelter B., Kurths J., Schulze-Bonhage A., Timmer J. Sensitivity and specificity of coherence and phase synchronization analysis. Phys. Lett. A 356, 2006, 26-34

[5] Schelter B., Winterhalder M. Kurths J., Dahlhaus R., Timmer J. Partial phase synchronization for multivariate synchronizing systems. Phys. Rev. Lett. 96, 2006, 208103

[4] Schelter B., Winterhalder M., Eichler M., Peifer M., Hellwig B., Guschlbauer B., Lücking C.H., Dahlhaus R., Timmer J. Testing for directed influences among neural signals using partial directed coherence. Journal of Neuroscience Methods 152, 2006, 210-219

[3] Schelter B., Winterhalder M., Hellwig B., Guschlbauer B., Lücking C.H., Timmer J. Direct or Indirect ? Graphical models for neural oscillators. J. Physiol. 99, 2006, 37-46

[2] Winterhalder M., Schelter B., Hesse W., Schwab K., Leistritz L., Klan D., Bauer R., Timmer J., Witte H. Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems. Signal Processing 85, 2005, 2137-2160

[1] Peifer M., Schelter B., Winterhalder M., Timmer J. Mixing properties of the Rossler system and consequences for coherence and synchronization analysis. Phys. Rev. E 72, 2005, 026213