The course will consist of four parts. In the first part we will deal with linear models and the related methods such as correlation functions and spektral analysis. At the end of this part we will deal with the Kalman filter, which is important also beyond the area of linear time series analysis.

After an intermezzo devoted to wavelet analysis we will proceed in the second part of the lecture to nonlinear deterministic systems and the corresponding methods, e.g. the estimate of fractal dimensions, dynamical entropies and Ljapunov exponents. Finally we will consider approaches to deal with nonlinear stochastic systems: Fitting Langevin equations or Fokker-Planck equations, respectively, from data.

If time suffices we will look at the end on different approaches to model physical phenomena directly, from cellular automata to partial differential equations.

Linear methods:

- Peter J. Brockwell and Richard A. Davis, Introduction to time series and forecasting, New York, Springer, 1996
- M. B. Priestley, Spectral analysis and time series, 9. printing, London, Academic press, 1996
- Peter J. Brockwell and Richard A. Davis, Time series : theory and methods, New York, Springer, 1991
- James D. Hamilton, Time series analysis, Princeton University Press, 1994

Nonlinear time series analysis

- H. Kantz and T. Schreiber, Nonlinear time series analysis, 2nd edition, New York, Cambridge University Press, 2004
- Henry D. Abarbanel, Analysis of Observed Chaotic Data, New York, Springer, 1997
- A concise introduction with a collection of classical papers: Coping with Chaos, ed. by Edward Ott, Tim Sauer and James A. Yorke, Wiley Series in Nonlinear Science, 1994
- For some more background on nonlinear dynamics: Edward Ott, Chaos in Dynamical systems, Cambridge University Press, 2nd ed., 2002

Stochastic Systems

- J. Honerkamp, Stochastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis, Wiley & Sons, 1993

- First lecture.
- Two lectures on linear models and spectral analysis.
- 9.05.: Lecture on filters and wavelets by A.Bergner.
- 16.05.: Introduction to nonlinear time series analysis - Embedding and dynamical invariants.
- 23.05.: Nonlinear time series analysis using TISEAN. Here are the slides from the lecture.
- 30.05.: Recurrence plot. Lecture by Norbert Marwan.
- 06.06.: Nonlinear time series analysis: Modeling and prediction, noise reduction and linear vs. nonlinear models. Slides from the lecture.
- 13.06.: From deterministic to stochastic systems. Linear or Nonlinear? Noise level estimation, surrogate data analysis and fittin Langevin and Fokker-Planck equations to data. Slides from the lecture.
- 20.06.: Interdependence measures --- cross correlation and coherence, mutual information, transfer entropy and synchronisation measures. Slides from the lecture.
- 27.06.: Extented computer lab including the time of the lecture.
- 04.07.: What to do with a given time series: Practical examples, e.g. EEG data. Slides.
- 11.07.: More exercises and computer lab on practical applications.
- 18.07.: Examination.

All chapters of the script of the first lectures in one file.