Homepage



 1. Nonlinear data analysis and modeling in sciences

 2. Probability distributions, statistical tests, correlation function,
    independence, stationarity, ergodicity, tests, likelihood fit, Chi2 fit,
    frequentist and Baysian paradigms, mutual information, Kolmogorov-Sinai-entropy, 
    periodogram, power spectrum, autoregressive models, wavelet analysis, principal component
    analysis, Kalman filtering, model estimation, Granger causality, transfer entropy,
    recurrence plots, embedding, estimation of fractal dimensions
    and entropies and Lyapunov exponents, local prediction, surrogate data method,
    measures of complexity.
    Models: ODEs, networks, ARMA processes, stochastic differential equations.

 3. Admission requirements:
    intermediate examination, lecture ``Nonlinear dynamics I & II''

 4. Optional compulsory course

 5. Prof. Dr. Arkadi Pikovski, Prof. Dr. Matthias Holschneider, Dr. Udo Schwarz

 6. Credit weighting:
    6 SWS all 
    2 SWS lecture
    2 SWS computer lab
    2 SWS practical

 7. Lecture and practical

 8. Course assessment:
    Solve exercises, written examination, certificate for regular and active participation

 9. German/English

 10. 9 ECT-points all

 11. Literature:
J. Honerkamp, Stochastic dynamical systems : concepts, numerical methods, data analysis 1994
Neil Gerschenfeld: The nature of mathematical modeling, Cambridge UP 1999
Kaplan: Statistical Modeling: A Fresh Approach 2009
Marek Fisz, Wahrscheinlichkeitsrechnung und mathematische Statistik
Bishop: Pattern recognition and machine learning, 2006
Papoulis & Pillai: Probability, random variables and stochastic processes 2002
Cover: Elements in information theory, 2006
von Storch & Zwiers: Statistical analysis in climate research, Cambridge UP 1999
Uwe Hassler: Stochastische Integration und Zeitreihenmodellierung - Eine Einführung mit Anwendungen aus Finanzierung und Ökonometrie
L. Sachs: Angewandte Statistik Methodensammlung mit R
Uwe Ligges: Programmieren mit R Statistik und ihre Anwendungen, 2009
Jens-Peter Kreiß and Georg Neuhaus: Einführung in die Zeitreihenanalyse
Reinhard Viertl und Dietmar Hareter: Beschreibung und Analyse unscharfer Information Statistische Methoden für unscharfe Daten, 2006
Hastie, Tibshirani, Friedman: Elements of statistical learning, 2001
Duda, Hart, Stork: Pattern classification, 2001
W.W.S. Wei, Time series analysis : univariate and multivariate methods 1994
P.J. Brockwell, Introduction to time series and forecasting, 1996
R. Schlittgen & B.H. Streitberg, Zeitreihenanalyse, R. Oldenbourg, M"unchen 1997
Christopher Chatfield: The analysis of time series : an introduction, Chapman and Hall, 1975, Teubner, 1982
Box, Jenkins, Reinsel: Time series analysis : forecasting and control, Prentice-Hall, 1994
James D. Hamilton: Time series analysis, Princeton Univ. Press, 1994
Sprott: Chaos and time-series analysis, Oxford Univ. Press, 2003
H. Kantz & T. Schreiber, Nonlinear Time Series Analysis, Camgridge University Press 1997 ** TISEAN 3.0.1:
http://www.mpipks-dresden.mpg.de/~tisean
H. Rinne, Taschenbuch der Statistik, Harry Deutsch 2003
W.H. Press, S.A. Teukolsky, W.T. Vetterling & B.P. Flannery: Numerical Recipes in C, Cambridge University Press 1993
Steeb: The nonlinear workbook 2008
Script

Homepage